Will Blog for Food

Social Choice Based Economic System Utilizing Range Voting

It has been shown that range voting offers a way out of Arrow's Impossibility Theorem. Arrow's Impossibility Theorem only applies to rank order voting methods and not point value methods. According to Arrow's book, "Social Choice and Individual Values," the field of social choice includes economic systems as well as voting systems. Since he thought social choice was impossible, no further discussion regarding economic systems was necessary. The assumed impossibility of social choice based economic systems was considered by some to be a theoretical endorsement of capitalism. However, Arrow had this to say about potential economic systems based on social choice, and since they are not as impossible as once was assumed, the topic is open for reconsideration:

THE ORDERING OF SOCIAL STATES

In the present study the objects of choice are social states. The most precise definition of a social state would be a complete description of the amount of each type of commodity in the hands of each individual, the amount of labor to be supplied by each individual, the amount of each productive resource invested in each type of productive activity, and the amounts of various types of collective activity, such as municipal services, diplomacy and its continuation by other means, and the erection of statues to famous men. It is assumed that each individual in the community has a definite ordering of all conceivable social states, in terms of their desirability to him. It is not assumed here that an individual's attitude toward different social states is determined exclusively by the commodity bundles which accrue to his lot under each. It is simply assumed that the individual orders all social states by whatever standards he deems relevant. A member of Veblen's leisure class might order the states solely on the criterion of his relative income standing in each; a believer in the equality of man might order them in accordance with some measure of income equality.

We will consider a potential economic system which abstracts from the general social choice model which Arrow considers but is related to it. We submit that it is a form of economic democracy in that it's based on range voting. We consider only a very simplified, hypothetical system which is impractical without the many ramifications necessary in the real world. However, it is necessary for the sake of analysis to abstract from many real world ramifications in order to get at the basic structure. In particular we consider an individually based system in which an "individual's attitude toward different social states is determined exclusively by the commodity bundles which accrue to his lot under each." We also simplify each commodity bundle so that it contains only "a complete description of the amount of each type of commodity in the hands of each individual [and] the amount of labor to be supplied by each individual." "[T]he amount of each productive resource invested in each type of productive activity" is determined by consumer demand as specified by the aggregate commodity bundles off all individuals. Furthermore, each individual submits an input regarding only his or her own work-consumption schedules, and not those he or she desires for other individuals. Finally, collective activity is abstracted from so that each possible social state represents the aggregate of the individual inputs regarding only their own work/consumption.

Each individual rates his or her preferred individual state on a scale such as [0-9] or [0-99], for instance, in accordance with range voting procedures. The social state is then determined in such a way as to maximize social welfare or utility as measured by the summation of ratings over individual states such that the following condition is met. In each possible social state, the work to be performed shall be exactly what is necessary to produce the commodities to be consumed. In other words supply of commodities shall be equal to demand for those commodities as specified by the ratings of individuals over all possible work-commodity bundles. For instance, individual A might rate a work-commodity bundle in which he performed 20 hours per week of dentistry (assuming he's qualified as a dentist) in return for a copious amount of goods and services a 99. He might also specify a rating of 50 for a work-commodity bundle requiring 30 hours work per week and a less copious amount of goods and services. He then might assign a 1 to a bundle requiring 60 hours work per week in return for a meager amount of goods and services.

THE ROLE OF MONEY IN A SOCIAL CHOICE ECONOMY

No real economic system could exist without money as a medium of exchange. It's just impractical to think that individuals would accept a system in which they were assigned a certain amount of work in return for a certain commodity bundle even if that maximized social utility. Therefore, work performed must be paid for in money and not by an "in kind" commodity basket. The commodity basket can be translated into monetary terms by pricing it such that the money received by each individual for his or her work exactly pays for it.  Pricing in such a system could be undertaken as follows. Pick some basic, simple and ubiquitous commodity and price it at 1 unit. (The units could be dollars, euros, pounds etc.) Then other consumer items could be priced in terms of that basic commodity considering the quantity and quality of labor and the quantity and quality of materials and other resources involved. For instance, a tube of toothpaste might be priced at 1 unit. Based on this, a particlular kind of automobile might then be priced at 20,000 units. Ideally, the aggregate amount of money dispensed by the system would be just sufficient to buy the aggregate amount of production as specified by aggregate consumer demand according to the the sum total of commodity bundles. Therefore, money supply would equal money demand, and there would be no inflation. Aggregate income could be computed in such a way that the amount of money in circulation would just be sufficient to buy all the consumer goods and services demanded according to the social state which maximizes social utility.

The social choice would then involve an assigment of work and income to each individual. It would be assumed that an individual's work preferences could be quite general involving different kinds of work and different hourly schedules. In general, an individual could do any type of work he or she was qualified for, and, at the lower end of the job spectrum, almost everyone would be qualified whereas at the upper end, only those with highly specialized training might be qualified. In general people would be qualified to do more than one type of work and would be free to submit more than one hourly schedule. Work weeks need not be standardized but could be individualized in accordance with worker demands. Since individuals might not spend their income exactly in accordance with the commodity bundle they submitted with the corresponding work schedule, aggregate consumption would have to be tracked and adjusted so that there is little or no over or underproduction.

Periodically, individual inputs regarding work-commodity bundles could be resubmitted, the social choice recomputed and adjustments made accordingly. Ideally, supply would equal demand both for work and commodities so that there would be no over or underemployment and no surplus or scarcity of commodities.

THE ROLE OF GOVERNMENT

Fundamentally, the role of government would be to gather information from individuals, compute the social choice, disburse information to individuals informing them of their work-commodity schedules and monetary income (the one that maximized social utility), and oversee and track the production and consumption process making adjustments for the fact that actual consumer demand might not be the same as specified consumer demand. The production units could be either publicly or privately owned. Individual work schedules could be combined to construct a production unit so that production units might represent the collaborative work efforts of many individuals and production output for the enterprise might represent enough commodities to fill many consumer commodity baskets. Individual or enterprise inputs might include capital or other resources as well as labor.

The government would have to employ the services of massive supercomputers to do all the computation necessary. Information collection and work-commodity bundle assigments would be centralized. Work schedule and consumer demands would be decentralized and individualized. Assigments would be flexible and subject to change both for work schedules and commodity bundle consumption schedules. The government could track changes in worker-consumer activity and make real time changes in production/consumption. The government might grant every citizen at least a minimum income for which could be purchased a minimum commodity bundle. A minimum amount of labor might also be required. Likewise, maximum work and/or consumer demands might be limited.

CONCLUSION

A social choice based economic system that utiilizes range voting has been described. Such a system would represent a highly simplified form of economic democracy. Individual work-commodity bundles would be preference rated in accordance with range voting and an amount of money associated with each. The system would then compute that social state which maximized social utility as the aggregate of individual utilites subject to the condition that production equal consumption. The system would also compute the pricing of consumption items and the amount of money to be distributed to each individual in return for the work and or capital resouces input by that individual. Money would just be a medium of exchange, and the total amount of money generated at any particular time would just be sufficient to buy the amount of production generated as specified by the social state which maximized social utility. Individual work-consumption assignments could be updated periodically or, perhaps, in real time in accordance with individual demands. Ideally, there would be no shortages or surpluses of commodities or labor and supply would equal demand. If priced correctly, supply would also equal demand in the money supply so there would be no inflation or deflation. There would be no unemployment by definition because exactly the amount of labor needed for production and no more would be required, and this would be distributed equitably by the maximizing of utility as a result of range voting.

A Districtless Congress

The US is divided up into political districts. Each voter gets to vote for one member of the House of Representatives and two members of the Senate in this bicameral national assembly. There are 435 voting members of the House so there are 435 congressional districts. The member from your district supposedly represents your interests, but none of the others do. In the Senate the political districts are the states. There are 100 senators, two from each state. The two senators from your state supposedly represent your interests but none of the other 98 do. So 1/435 or 0.22% of the members of the house represent your interests, and 2/100 or 2% of the members of the senate represent your interests.

This is a pathetic situation, and it's even worse if you did not vote for any of the congressman or senators who supposedly represent you. Say you're a Democrat and the congressman elected from your district (whom you didn't vote for) is a Republican. Then arguably you have no representation at all in the House. The same could be said of the Senate if you didn't vote for either of the senators who actually got elected. In other countries where they use other methods for making up the national assembly or congress like, for example, proportional representation, the percentage of the members representing each voter's interests is much higher. For example, if 28% of the electorate (including you) voted for the Green Party, then 28% of the seats in the national assembly would be Green Party members.

In a districtless congress each voter would vote for each representative, and each representaive would represent the interests of all voters. For example, if there are 300 seats in the congress and 500 candidates running for those seats there would be 500!/(300!)(200!) possible congresses or ways that this congress could be made up. In theory each voter could list each possible congress in order of his/her preferences, and then all the voters' specifications could be amalgamated to get the one congress that best represented the electorate as a whole. The problem is that it would be impractical for each voter to study the qualifications of each candidate and then come up with a list of all possible congresses. It would be too much work. However, there are ways to expedite this process as explained in more detail here. If each voter just listed the candidates (instead of the congresses) in order of preference, this list could be translated by software into an ordered list of congresses. Furthermore, the list of candidates could be simplified by using the recommend- ations of the voter's political party or other trusted experts in part or in whole. A customized list could be generated by taking eclectic recommend- ations cafeteria style. Or there could be different lists available to the voter depending on the voter's profile related to his/her political objectives. A simple questionnaire given to the voter could generate a list according to the voter's predilections. There are a lot of different ways any particular voter's list could be generated with the voter having complete control and the final say.

One way of amalgamating the list information is by range voting. Using this method each possible congress would be given a numerical rating, and the ratings for each congress would be added up over all the individual voters to determine the winner - the one with the highest overall social rating. There is no need to rank the possible congresses in order over the entire electorate since only the top rated one would be chosen. Therefore, Kenneth Arrow's model for social choice and his impossibility results as presented in Social Choice and Individual Values are invalid.  In fact Arrow's model which calls for a full social ranking doesn't apply to most political as well as most economic situations. The only thing it seems to apply to is combining judges' rankings in Olympic figure skating where it is important to know not only first place but also second and third. In political and economic situations it's necessary only to know the top rated or first place result.

Fractal Voting

Fractal Voting (FV) is a voting method I developed. It is one of a class of utilitarian methods similar to range voting (RV) in some respects. Other utilitarian methods are approval voting (AV) and Evaluative Voting (EV). RV, AV and EV are all special cases of FV. Utilitarian voting methods involve a ranking of candidates or alternatives from most preferred to least preferred. In general there are two types of rankings: ordinal and cardinal. Ordinal ranking involves a list such as ABCD where the position of the letter, for example, indicates its preference ranking in this case A is preferred to B is preferred to C etc. Cardinal ranking also indicates how much A is preferred to B and how much B is preferred to C etc. This "how much" is also referred to as preference intensity. With utilitarian methods  numbers are usually asssigned to the candidates and the differences between the numerical rankings of two candidates indicate the preference intensity. One of the differences between FV and RV is that voters don't assign numbers to the candidates but indicate  preference intensities graphically.

Fractal Voting consists of a graphical user interface (GUI) or we could call it a graphical voter (GVI) interface (we will use the terms voter and user interchangably) and underlying software which translates the voter's preferences into numerical values which can then be used to sum up the votes for  each candidate and  determine the winner. Range Voting involves a system defined scale such as 0-99, 0-9 etc. The voter assigns a number contained in this scale to each candidate, and then the numbers are summed for each candidate to determine the winner. With Fractal the voter determines the scale and the scale can be more finely determined or less finely determined in different segments as the voter wishes. For example, if the voter wants to differentiate among candidates near the top of the scale more finely, he or she can subdivide that portion of the scale more finely in order to make these distinctions. The fineness of the scale is called the sensitivity level.  The sensitivity level, in general, will differ for each voter depending on how finely a voter can distinguish between two candidates or alternatives. This concept can be generalized to include fine distinctions between tastes or smells for example. A person might be asked to distinguish and rank several wines. Some people would be able to distinguish them very finely and others would only be able to make rough distinctions, say between good and bad. With RV, the system defines the sensitivity level which is the same for all voters. RV with a scale 0-99 has a higher sensitivity level than RV with a scale 0-9 and allows finer distinctions among candidates to be made. For example, candidates A and B might each be given ratings of 5 with RV (0-9) but given ratings of 51 and 57 with range (0-99). So finer distinctions can be made the more levels are available. 

With Fractal, the user or voter has complete control over the sensitivity which is variable over the whole scale. For instance, at the beginning of the voting process, the first thing a voter would do is to choose the number of levels he or she would like to start out with. This might be just two - good and bad. So there would be two "buckets" if you will, the good bucket and the bad bucket. All candidates in the good bucket would be indistinguishable from or indifferent to each other. However, before choosing the number of levels or buckets, the voter would first choose their most preferred or favorite candidate or candidates and least preferred candidate or candidates. Then all others would be relative to those. So initially a screen would be presented to the voters with two buckets - one for most preferred and one for least preferred. The voter would drag appropriate candidates onto these buckets from a list arbitrarily located on the right side of the screen. Then the voter would choose how many buckets or levels to start with. Please note that, if the voter chose 100 buckets and didn't go any deeper or finer than that in terms of sensitivity level, the voting method would be the same as RV. After the initial choice of number of buckets, that number of buckets appears on the screen as well as the buckets at either end denoting most preferred and least preferred. Now the voter drags other candidates from the list onto the buckets. Then the voter has the option of clicking on any one of the buckets and further subdividing this segment of the  scale. Let's say that the voter started with 10 buckets, and, in all but one bucket, there is only one candidate. In one bucket there are 4 candidates. The voter may choose to click on that bucket and then choose to subdivide that bucket alone into, for instance, 4 finer levels. These buckets then appear on the screen along with the list of the candidates who were in the original bucket. The voter then drags candidates from this list onto one of the buckets that represent subdividions of the original bucket. This process can be repeated indefinitely leading to finer and finer distinctions. When the voter is satisfied he or she can terminate the process and submit his or her vote.

The final vote can be printed out as a paper ballot showing an overall scale subdivided as the voter has indicated and all candidates listed in order of preference, preference intensity and fineness of distinction or sensitivity. The underlying software can be implemented in terms of a push down stack where the first word in the stack contains the number of words in the stack. Initially, this would be 2 for most preferred and least preferred. These words might contain the numbers 1 and 0, respectively. As the voter adds levels or buckets, words are added to the stack.  The stack would be popped up to the level where the voter indicates that he or she wishes to add levels, and then the number of levels added that the voter has indicated. For instance, if the voter initially wants to order candidates just in terms of good and bad (a binary decision), two words would be added to the stack between the words corresponding to least preferred and most preferred. One might contain the number 1/4 (corresponding to the mid-point of the "bad" bucket) and one might contain 3/4 (corresponding to the mid-point of the "good" bucket). Continuing on in this way, the buckets are each defined in terms of a numerical value in a process that is totally transparent to the voter who just has to deal with a simple GUI and repeat the same process over and over to as many levels as he or she wishes. Then each candidate is associated with a pointer that points to the appropriate numerical value in the stack.

Since the process is the same for the voter no matter how deeply he wishes to proceed in terms of sensitivity level, we call this method Fractal Voting. Think of it as branches on a tree some of which are subdivided into smaller branches which are further subdivided and so on. At each stage the voter performs the same steps so the process is simple and intuitive for the voter.  This is the essence of the fractal process: no matter what the depth, the procedure is the same. At completion each candidate will be asssociated with a pointer which represents his numerical rank. The pointer will point to a word in the stack which will contain a value between 0 and 1 which represents the intensity  of that rank. Note that, unlike RV, the voter never has to assign numerical values to candidates making the provess simpler and more intuitive akin to punching a hole on a ballot or putting a check mark next to a candidate. When all voters have submitted their ballots, the numerical values associated with each candidate are summed and the one(s) with the highest value win(s).

The advantages of Fractal over Range are the following:

1) There are no "partial strength" votes. A partial strength vote is submitted in Range when a voter does not pin his most (least) preferred candidates to the limits of the range.

2) The voter has a simpler and more intuitive while at the same time more sophisticated interface which allows him or her more options in the voting procedure.

3) The voter can choose his or her own sensitivity level and can continue to refine this as the voting process continues.

4) The voter can go into detail selectively in those parts of the overall ranking that concern him or her while doing a rough ranking in other parts of the overall scale.

5) The voter need not be concerned with numbers at all, but only with a visual on-screen representation of the preference rankings and intensities.

Fractal Voting lends itself to delegable proxies since various parts of the tree could be designated and filled in by trusted parties who have pre-voted and whose results are only a mouse click away. For instance, the voter could select certain candidates, indicate he wished to make a proxy vote and then select Ted Kennedy from a list of proxies. Then these candidates would be added to the screen in exactly the way that Ted Kennedy had previously indicated he would vote. This method would lend itself either to touch screen or computer screen voting. Security of the vote could be guaranteed by different methods, but this is really a separate issue. Issuance of a paper ballot and receipt would be a start.

In summary Fractal Voting is a generalization of AV, EV and RV and a voter could choose to vote in any of these styles if so desired. It is a utilitarian voting method since the placing of each candidate on a line in order of preference ranking and intensity reveals the voter's utility for each candidate in some sense. Social utility could be measured for each candidate by simply adding up the numerical values asssociated with that candidate in the stack over all voters. This would not represent a social utility in an absolute sense but in a relative sense. The voter is allowed to make either fine or rough distinctions among the candidates according to his or her sensitivity levels and/or knowledge of the candidates, and also to rely on the advice of trusted experts who have studied the issues and/or candidates more closely. Both the GUI and the underlying software are easily implemented.

Arrow's Take on the "Ordering of Social States"

The following quote is taken from "Social Choice and Individual Values" by Kenneth Arrow, pp. 17-18. This represents Arrow's conception of an economic system rather than a political or voting system. Please notice that Arrow requires each individual to submit his preferences regarding not only his own work and consumption preferences but also his preferences regarding everyone else's work and consumption thus making this system totally impractical and unviable. He calls ordering everyone else's work and consumption "ordering according to values" while just ordering preferences regarding one's own work and consumption "ordering according to tastes." In this economic system one could submit preferences that one's enemies should work 80 hours a week for starvation wages and one's friends and cronies should get CEO salaries for doing practically nothing! One could submit preferences that one's self and friends should get $7 - $10 million a year for attending parties as Paris Hilton does!

Any viable economic system would only require that each individual submit preferences regarding one's own preferred patterns of work and consumption, but this would depart from the model Arrow uses for proving that social choice is impossible. The part about each individual specifying preferences regarding "collective activities" is completely viable. These are such things as public parks, public libraries, public education and, in most advanced countries other than the US, public health care. The individual would also submit preferences regarding how much he personally would be willing to pay as his part for such activities. This is commonly known as taxation. While Arrow goes on and on about tastes and values, he elaborates very little about "collective activites" which could be a valid part of an individual's preference specifications.

An economic system based on amalgamating data from each individual and treating each individual equally would be a form of economic democracy. Also it may escape Arrow's proof that social choice is impossible because it departs from his model by virtue of the fact that each individual does not submit preferences about social states but only about his own personal and social consumption and willingness to work to support such consumption. Thus an analysis of the viability of this model might show that it is not impossible given a set of "rational and ethical criteria" (not necessarily the same set as Arrow uses to prove social choice impossible).

The following is the quote from Arrow:

THE ORDERING OF SOCIAL STATES In the present study the objects of choice are social states. The most precise definition of a social state would be a complete description of the amount of each type of commodity in the hands of each individual, the amount of labor to be supplied by each individual, the amount of each productive resource invested in each type of productive activity, and the amounts of various types of collective activity, such as municipal services, diplomacy and its continuation by other means, and the erection of statues to famous men. It is assumed that each individual in the community has a definite ordering of all conceivable social states, in terms of their desirability to him. It is not assumed here that an individual's attitude toward different social states is determined exclusively by the commodity bundles which accrue to his lot under each. It is simply assumed that the individual orders all social states by whatever standards he deems relevant. A member of Veblen's leisure class might order the states solely on the criterion of his relative income standing in each; a believer in the equality of man might order them in accordance with some measure of income equality. Indeed, since, as mentioned above, some of the components of the social state, considered as a vector, are collective activities, purely individualistic assumptions are useless in analyzing such problems as the division of the national income between public and private expenditure. The present notation permits perfect generality in this respect . Needless to say, this generality is not without its price. More information would be available for analysis if the generality were restricted by a prior knowledge of the nature of individual orderings of social states. This problem will be touched on again. In general, there will, then, be a difference between the ordering of social states according to the direct consumption of the individual and the ordering when the individual adds his general standards of equity (or perhaps his standards of pecuniary emulation).14 We may refer to the former ordering as reflecting the tastes of the individual and the latter as reflecting his values. The distinction between the two is by no means clear-cut. An individual with esthetic feelings certainly derives pleasure from his neighbor's having a well-tended lawn. Under the system of a free market, such feelings play no direct part in social choice; yet psychologically they differ only slightly from the pleasure in one's own lawn. Intuitively, of course, we feel that not all the possible preferences which an individual might have ought to count; his preferences for matters which are "none of his business" should be irrelevant. Without challenging this view, I should like to emphasize that the decision as to which preferences are relevant and which are not is itself a value judgment and cannot be settled on an a priori basis. From a formal point of view, one cannot distinguish between an individual's dislike for having his grounds ruined by factory smoke and his extreme distaste for the existence of heathenism in Central Africa. There are probably not a few individuals in this country who would regard the former feeling as irrelevant for social policy and the latter as relevant, though the majority would probably reverse the judgment. I merely wish to emphasize here that we must look at the entire system of values, including values about values, in seeking for a truly general theory of social welfare. It is the ordering according to values which takes into account all the desires of the individual, including the highly important socializing desires, and which is primarily relevant for the achievement of a social maximum. The market mechanism, however, takes into account only the ordering according to tastes. This distinction is the analogue, on the side of consumption, of the divergence between social and private costs in production developed by Professor Pigou.15 14. This distinction has been stressed to the author by M. Friedman, The University of Chicago. 15. A. C. Pigou, The Economics of Welfare, London: Macmillan and Co., 1920, Part II, Chapter VI. For the analogy, see Samuelson, op. cit., p. 224; Reder, op. cit., pp. 64-67; G. Tintner, "A Note on Welfare Economics," Econometrica, Vol. 14, January, 1946, pp. 69-78.

Range Voting

A little known or discussed fact of life in the US is that, while we are a younger nation than most European countries, our constitution and our voting system is older than any of theirs. Why? Because they have updated their constitutions and/or voting systems while ours have remained static since their inception over 200 years ago. While other countries have taken the pragmatic view that upgrading (taking into account advances in voting theory) might be a good idea, our voting system along with all other aspects of our constitution (not to mention our economic system) might as well have been set in stone. To even question their continued validity or possible improvement is considered by some to be unpatriotic.

Our voting system is called plurality voting. This means that only one candidate out of however many are running for office is chosen by each individual voter, and then the votes are tallied and the one with the most votes wins providing he or she has a sizable enough percentage of the total votes cast. Otherwise there's a runoff. The literature is full of the pitfalls of this method of voting. Suffice it to say it practically eliminates more than two parties. Another disadvantage of our political system is that the US is divided up into districts with each district returning one representative to the bicameral House while each state returns two Senators to the Senate. So each voter is represented in Congress by only three people: one member of the House and two Senators. That's a very small proportion of the total number of lawmakers when you consider that there are 435 Congressmen and women in the House and 100 Senators. 3 out of 535? 0.5%? How does that make you feel, voters, to know that less than 1% of the lawmakers in Washington represent you or that you had anything to do with electing them? In addition there are the problems of the Electoral College (the President is not elected by a direct vote of the public) and gerrymandering which is an artificial way of dividing up political districts in such a way that favors one party or another. Of course, the party in power gets to do this in order to guarantee itself as many seats in perpetuity as possible. A more sensible way to choose a President is by a majority of all the votes cast eliminating the Electoral College altogether, and a more sensible way of choosing legislators would be a system in which each voters gets a chance to vote for more than three legislators.  

Fortunately, voting theorists have not been inactive. There are at least three methods which promise to be an improvement over the current state of affairs vying for the hearts and minds of the public - at least some members of the public, the cognoscenti, who have bothered to consider such things: range voting (RV - not to be confused with those behemoth gas guzzlers), instant runoff voting (IRV) and approval voting (AV). Each method has its supporters, defenders, detractors, protagonists, antagonists and critics. Approval voting is simple enough. Instead of voting for one out of however many candidates are running, you vote for all the  candidates you approve of. Instead of marking the ballot once in each race, you mark it multiple times. Obviously, it wouldn't make sense to mark it for every candidate who is running although I'm sure there are many who would. IRV is more complicated, but you can Google it and find out more than you really wanted to know. That leaves range voting.

You are already familiar with it as this is the method used to score Olympic athletes. You would rate each candidate on a scale from 1 to 10 or 0 to 20 or -99 to +99. The actual limits to the range are somewhat arbitrary as long as each voter can assign ratings over the same range. Then you tote up the score for each candidate and the one with the most points wins. Or you can take the average and the one with the highest average wins. There is one refinement, however, with reference to the above linked website. You do not have to actually vote for each candidate. If there are 100 running and you actually rate only 50 filling in an X for the remaining fifty, then the average is computed by dividing the total (over all voters) votes cast for a candidate divided by the sum of all the voters who actually cast a vote for that candidate (Xs excluded). A candidate needs a quorum of votes to win where a quorum is defined as half the total points of the highest point getter. So, theoretically, a candidate with half the total points of the highest total point getter could win the election if sufficiently few voters actually voted for him or her while sufficiently many voters put down an X for him or her. This seems to introduce a certain amount of arbitrariness to the method, but, obviously, something would have to be done to prevent a candidate whom only a handful of voters voted for (all presumably giving him the highest score) from winning. An alternative way of handling this situation would be to just use total point scores forcing each voter to make a decision regarding each candidate. For candidates unfamiliar to any particular voter, that voter could use a proxy rating. A proxy rating would be provided by an expert of the voter's own political persuasion or someone trusted by the voter who is familiar with the candidate. It could be a rating provided by the voter's political party. Without having done an extensive analysis, this seems somewhat less arbitrary to me. 

Donald Saari is a proponent of the Borda count. Steven Brams is a proponent of Approval Voting and Warren D Smith is a proponent of Range Voting. I also independently came up with a version of range voting which I called the Lawrence Count. Due to the serendipity of the internet, someone perusing my website, Social Choice and Beyond, brought to my attention that, unbeknownst to me at the time, there exists a major website promoting and expounding on a similar voting method. Thus are like-minded people all over the world brought into contact with one another thanks to the world wide web! This is truly amazing! As I said on my webpage: "The Lawrence Count is a modified Borda Count which seems so obvious that maybe someone has already discovered it. If so, I relinquish the name and any claim to being its progenitor." So I will change my webpage to indicate that I'm no longer pretentious enough to name something after myself especially if someone else has already discovered it. By the way Warren D Smith doesn't claim to have discovered it either so  I guess it was too obvious for anyone to have discovered it, and Smith claims that actually the ants and honey bees discovered it.

The three gentlemen named above go round and round trying to prove that their method is the best and showing the pitfalls of all the others. My opinion is that approval voting is a step above plurality voting but is too simple to take into account the range of expression a voter may wish to demonstrate. It's as if Olympic ice skaters were either approved or disapproved by the judges and then their scores computed. Would you be satisfied with that? The Borda count is too rigid. It has the anomaly that, if one candidate drops out of the race, point values must be reassigned with the result that someone could win who previously was ranked last. Range Voting, in my opinion, is a modified Borda count in that the underlying grid remains constant whether or not candidates enter or drop out of the election. Point values remain the same except for some strategic considerations which, again in my opinion, the voter has a right to take into consideration. There is maximum expressivenesss in that the voter not only gets to rank the candidates but also gets to indicate to an extent how much he or she favors one over another. If each voter gives his or her most favored candidate the highest possible score and his least favored the lowest posssible, then he or she will be getting the most strategic value out of his or her vote. If there is one candidate who is so horrible compared to all the others in the mind of a particular voter, it would not only be honest but strategically advantageous to give the horrible candidate a zero and all others the highest possible rating. Likewise, if there is one candidate who is far and away the most superior compared to the other candidates, it would be honest and strategic to give that candidate the highest rating and all others a zero. Another point is that the point spread from lowest to highest score (say 1 to 99) need only be as great as the sensitivity of the most sensitive voter where sensitivity is defined as the most perceptive voter's ability to make a one point distinction between two candidates. Presumably some voter would be able to rate some candidate in a meaningful way as a 53 and another as a 54, for example.

One reason for the lack of agreement regarding voting methods is Arrow's Impossibility Theorem which states in general terms that there is no democratic voting system which obeys certain rational and ethical criteria. This has given rise to the field of social choice theory. Not everyone would agree with Arrow's choice of rational and ethical criteria but, be that as it may, in over 60 years no one has been able to show that Arrow didn't know what he was talking about. So even if in some sense democratic voting systems are impossible, elections are still held and some voting methods are definitely better than others, and, even though there is no general agreement, there is still hope that we will be able to do better in the future than we have done in the past. Hope springs eternal!

Choice

A recent book, The Paradox of Choice, by Barry Schwartz, argues that, as choices proliferate, people are less satisfied overall. He says that we would be better off and more satisfied if we had fewer choices. I think his analysis is fairly shallow and he misses the mark. A lot of the book is "filler" which one has come to expect from a best seller. This book claims to have been a "Business Week Top Ten Book of the Year." His book is long on pseudo-psychological psycho-babble and short on the analysis of social conditions such as advertising which distort the whole process of choosing and turn many choices into phony or false choices which benefit only the seller, not really the consumer.

A social system such as preferensism which is an outgrowth of social choice is predicated on the assumption that increased freedom is associated with increased choices, and, I would argue, that increased choices are increasingly satisfying provided that the choices are real and not distorted by advertising. In addition, there are methods and techniques (hardly mentioned by Barry Schwartz) for dealing with what might seem like a bewidering array of choices. For example, before I purchase a CD, I read reviews (hopefully more than one) to see what the critics have to say about the music. I know from experience that I'm particularly interested in only one genre of music so that eliminates a large number of choices that I don't even have to consider right there. Consumer Reports as well as a number of online services such as epinions rate and rank different products, and there are price comparison wesites such as shopping.com that do price comparisons.

Therefore, I feel there are intelligent ways of making a decision as to which product or service one wishes to consume which make the process rewarding if not enjoyable. The only depressing thing to me is having my programming interrupted by TV and radio advertising. That, not the number of choices available, is what is truly depressing. Schwartz walks into a store and notes that there are "285 varieties of cookies," "40 options for toothpaste" etc. Unfortunately, he never gets beyond a rather psychological analysis as to why there are such a bewildering number of options and are any of the options any good? I have been on a quest to find plain white toothpaste like used to be on store shelves when each manufacturer was represented by only one variety of toothpaste. Although there are 40 varieties of toothpaste, I have not been able to locate on the store shelves just plain white toothpaste. The question is why? I think the answer has to do with (of all things) the marketing clout of the large toothpaste producing corporations. Crest and Colgate are the two largest and they have the most varieties of toothpaste taking up the most shelf space real estate in the supermarket. Inside the boxes, which tout the different varieties, the toothpaste is remarkably similar. For the most part it is all an aqua color which leads me to believe that the only significant difference among the different varieties is the packaging.

Now the supermarket will not devote a large amount of shelf space to just one variety of toothpaste. For a company to dominate the supermarket shelves, they have to produce what seemingly is a large number of different kinds of toothpaste. The only problem is they're not really all that different. So these choices are false choices. They're not really giving consumers a large number of choices at all, just attempting to dominate supermarket real estate, and evidently, the supermarkets are happy to go along with this deception.

Another problem in the "bewildering array of choices" that Schawarz notices is that in many cases hardly any of them are of high quality. I've noticed time and again a product, that I had been a regular purchaser of because I really liked the product, disappearing from store shelves only to be replaced by a similar but less desirable product. Why do you suppose this is and how does this affect Schwartz' rather depressing analysis that more choices produce less satisfaction? My analysis is that the store manager only wants to devote shelf space to products for which there are the highest profit margins. Therefore, a lower quality product which costs less to produce may have a higher profit margin than a high quality product whose ingredients cost more. Such a product may have a lower profit margin. And through advertising, corporations can increase demand for low quality products which have high profit margins. This is why independent testing and rating agencies are so important. Expert opinion and criticism can defeat the purpose of advertising which is to increase corporate profit margins, not to educate or inform the consumer, let alone provide him or her with a quality product.

Companies which put out a high quality product can take market share from companies who have established a "brand" but continue to market the lowest quality the consumer will buy. Take coffee, for instance. The coffee industry has known for years that there are two kinds of coffee beans: the low quality and cheaper Robustico and the higher quality and more expensive Arabica. Naturally they sold the lower quality coffee and made hefty profits for years. Then along came Starbucks and their goal was to deliver a superior product. They, therefore, used the higher quality and more expensive ingredients. Their profit margin per cup might have been lower, but they gained enormous market share because consumers, once they had been exposed to a superior product, came to be willing to spend more to get an excellent cup of coffee rather than the swill they had been used to. The same thing could be said for bread. People who were fortunate enough to travel to Europe where the quality of bread and coffee was superior saw the opportunity for emulating those operations and establishing high quality niche markets.

So I think Mr. Schwarz totally misses the mark. Instead of an analysis of the false choices that are so depressing, he tells us that more choice in general is depressing. His agent must have told him to include the psycho-babble in order to sell books. But it's basically bullshit. Most people that are at all sophisticated or experienced make choices based on their experience and rely on expert opinions from knowledgable sources. Smart people today can avail themselves of resources widely available on the web to make choices. There are quality comparison sites and price comparison sites. Instead of giving an intelligent method for culling the bad choices and narrrowing down to the good quality choices, Mr. Schwarz just says that we should have fewer choices in general and then we would be better off. I disagree. I think we are better off when we have an increasing number of high quality choices.

In a society based on preferensism, choice is fundamental. A citizen has to make choices which are both political and economic in nature. The educational system in any society needs to teach people how to make intelligent choices. For instance, in a political system in which all candidates for the Senate are voted on by all voters instead of just voting on a district by district basis, obviously there would be many more choices to consider than if one were just voting for one senator from one district. Such a system could still make sense and increase the freedom of each citizen if citizens allowed themselves to be guided in making choices the way they are guided by critics and experts in making consumer choices. A party or publication might make recommendations based on their way of thinking and each voter might take the recommendations of the party or publication they felt an affinity with.

There are other ways to make choice manageable in a preferensist society or one based on individual and social choice. A good review of some of these ideas can be found here.

Arrow's R Notation

Arrow's R Notation

In the arcane world of social choice, a man by the name of Kenneth Arrow looms large. In 1951 he published a book, "Social Choice and Individual Values," in which he supposedly proved that social choice is impossible. But what is social choice? Let us say we have a society composed of N individuals numbered 1,2,3, ... . Those individuals have to order a set of M alternatives with their most preferred alternative being their first choice etc. Let's indicate the alternatives as a, b, c, ... . Then a social welfare function accepts the individual orderings as inputs and produces as output the social ordering which is an ordering of the alternatives that applies to the whole society.

If individual 1 prefers a to b, we write aP1b. If society prefers a to b, we write aPb. So far so good. But we also want to provide for the case in which an individual is indifferent between a and b. We write this aI1b and aIb, respectively. Arrow's analysis then combines these two relationships into a relationship he denotes as R which means "prefers or is indifferent to" so aR1b means individual 1 prefers a to b or is indifferent between a and b. Arrow's rationale for this is the following: "Instead of working with two relations, it will be slightly more convenient to use a single relation, 'preferred or indifferent.'" (p. 12) (emphasis added)

Arrow then goes on to postulate two axioms. Axiom 1 states that either xRy or yRx and he notes that this does not exclude the possibility that both xRy AND yRx. Axiom 2 has to do with transitivity which will not concern us here. Again Arrow states (p. 13): "Axioms 1 and 2 do not exclude the possibility that for some distinct x and y, both xRy and yRx. A strong ordering on the other hand, [one with only preferences and without indifferences] is a ranking in which no ties are possible." This is blatant nonsense. One could have half the population with xPy and half with yPx [strong orderings] and that certainly would represent a tie so a tie is possible. What Arrow is implying without coming out and saying it directly is that in his world a tie between two alternatives is to be represented as a social indifference. This is completely arbitrary and limits his entire analysis.

One must assume that in Arrow's world each individual will submit his input in terms of R. That is individual 1 would submit aR1b, aR1c etc. until all pairwise comparisons have been made. For now we will go along with Arrow's demand that only pairwise comparisons need to be submitted. It can be assumed that individuals are not permitted to submit a comparison using the indifference relation since then what would be the purpose of introducing R to make the analysis "slightly more convenient." The whole idea of "slightly more convenient" is to reduce the number of relations from 2 (P and I) to 1 (R). However, Arrow proposes (without saying so) to use the I relation in the social choice to cover the case of a tie. Therefore, the social choice could be aRb, bRa or aIb.

Now the idea of the social welfare function (or of any function for that matter) is to connect each element of the domain (consisting of all possible combinations of individual choices) to an element of the range (consisting of all possible social choices). There are a great number of possible functions. Each function will hook up elements of the domain with elements of the range differently. The important thing is that each possible element of the domain is hooked up to one and only one element of the range. Arrow implies that any element of the domain that represents a tie (such as half the population having aRb and half having bRa) should be hooked up with the range element aIb. Respectfully, I disagree with this approach for the following reason: the half of the population that has aRb could actually prefer a to b (no one is indifferent), and the half of the population that has bRa could actually prefer b to a. That represents a tie to be sure, but society is hardly indifferent between the two alternatives. Arrow has confused a tie with an indifference! By so doing he has guaranteed that his analysis will yield the result that no social choice is possible.

Secondly, I would like to point out that individual information is lost when an individual submits his input as aR1b or "I prefer a to b or I'm indifferent between a and b." The system does not know which, and this introduces ambiguity at the outset. Not only that, but say an individual is indifferent between a and b. He has two ways to express it! He can submit either aR1b or bR1a. The resulting analysis becomes meaningless as the system knows not how many of the individual aRb's represent indifferences and how many of them represent preferences. Ditto for the individual bRa's! There can be no meaningful social welfare function given these kinds of inputs.

Therefore, I suggest that Arrow's approach is not acceptable and that his conclusion that social choice is impossible is invalid. A more rigorous approach is necessary involving the possibility of ties between orderings as elements of the range.

Here's a link to a blog which quotes from my website Social Choice and Beyond:  Solving the Tyranny of Choice.

Arrow's R Notation Continued

We promised to do an examination of Arrow's R notation to resolve the differences between my friend, Ben at Oxford, and myself. Ben contended that R was only a "representation device." (See Comments.) After delving into this subject I would both agree and disagree. Arrow says on p. 12 of “Social Choice and Individual Values”: “Preference and indifference are relations between alternatives. Instead of working with two relations, it will be slightly more convenient to use a single relation. ‘preferred or indifferent.’ The statement ‘x is preferred or indifferent to y’ will be symbolized by xRy. The letter R, by itself, will be the name of the relation and will stand for a knowledge of all pairs such that xRy.” [emphasis added]

So R is both a representation device (when it stands alone) and a logical relation when it stands between two letters representing alternatives. A relation of the form aPbPcIdPf... (where a,b,c... stand for alternatives; P stands for preference and I stands for indifference) makes perfect sense since the logical relationships are clear. However, a relation of the form aRbRcRdRf... makes no sense since one must know the truth values of aRb and bRa, aRc and cRa, aRd and dRa etc. etc.

We have assumed that Arrow’s intent was to maintain a 1-1 relationship between P and I, on the one hand, and R on the other so that individual voters would submit their ballots in terms of P and I. These ballots could then be translated to terms of R as long as one knew both xRy and yRx. The dichotomy between the two notations is that one only need know xPy, yPx or xIy since they are all mutually exclusive. If you know that xPy is true, for example, you need not know the truth values of xIy or yPx. However, you do need to know the truth values for both xRy and yRx in order to maintain the 1-1 relationship between R and {P,I}.

We think that it is more transparent and less confusing to use the P and I notation instead of the R notation . Arrow’s use of the R notation because it is, according to him, “slightly more convenient,” turns out to be more cumbersome and more confusing. The same proofs could be done using P and I instead of  R. The in-depth analysis of this conumdrum continues here.

Arrow's R Notation

In the arcane world of social  choice, a man by the name of Kenneth Arrow looms large. In 1951 he published a book, "Social Choice and Individual Values," in which he supposedly proved that social choice is impossible. But what is social choice? Let us say we have a society composed of N individuals numbered 1,2,3, ... . Those individuals have to order a set of M alternatives with their most preferred alternative being their first choice etc. Let's indicate the alternatives as a, b, c, ... . Then a social welfare function accepts the individual orderings as inputs and produces as output the social ordering which is an ordering of the alternatives that applies to the whole society.

If individual 1 prefers a to b, we write aP1b. If society prefers a to b, we write aPb. So far so good. But we also want to provide for the case in which an individual is indifferent between a and b. We write this aI1b and aIb, respectively. Arrow's analysis then combines these two relationships into a relationship he denotes as R which means "prefers or is indifferent to" so aR1b means individual 1 prefers a to b or is indifferent between a and b. Arrow's rationale for this is the following: "Instead of working with two relations, it will be slightly more convenient to use a single relation, 'preferred or indifferent.'" (p. 12) (emphasis added)

Arrow then goes on to postulate two axioms. Axiom 1 states that either xRy or yRx and he notes that this does not exclude the possibility that both xRy AND yRx. Axiom 2 has to do with transitivity which will not concern us here. Again Arrow states (p. 13): "Axioms 1 and 2 do not exclude the possibility that for some distinct x and y, both xRy and yRx. A strong ordering on the other hand, [one with only preferences and without indifferences] is a ranking in which no ties are possible." This is blatant nonsense. One could have half the population with xPy and half with yPx [strong orderings] and that certainly would represent a tie so a tie is possible. What Arrow is implying without coming out and saying it directly is that in his world a tie between two alternatives is to be represented as a social indifference. This is completely arbitrary and limits his entire analysis.

One must assume that in Arrow's world each individual will submit his input in terms of R. That is individual 1 would submit aR1b, aR1c etc. until all pairwise comparisons have been made. For now we will go along with Arrow's demand that only pairwise comparisons need to be submitted. It can be assumed that individuals are not permitted to submit a comparison using the indifference relation since then what would be the purpose of introducing R to make the analysis "slightly more convenient." The whole idea of "slightly more convenient" is to reduce the number of relations from 2 (P and I) to 1 (R). However, Arrow proposes (without saying so) to use the I relation in the social choice to cover the case of a tie. Therefore, the social choice could be aRb, bRa or aIb.

Now the idea of the social welfare function (or of any function for that matter) is to connect each element of the domain (consisting of all possible combinations of individual choices) to an element of the range (consisting of all possible social choices). There are a great number of possible functions. Each function will hook up elements of the domain with elements of the range differently. The important thing is that each possible element of the domain is hooked up to one and only one element of the range. Arrow implies that any element of the domain that represents a tie (such as half the population having aRb and half having bRa) should be hooked up with the range element aIb. Respectfully, I disagree with this approach for the following reason: the half of the population that has aRb could actually prefer a to b (no one is indifferent), and the half of the population that has bRa could actually prefer b to a. That represents a tie to be sure, but society is hardly indifferent between the two alternatives. Arrow has confused a tie with an indifference! By so doing he has guaranteed that his analysis will yield the result that no social choice is possible.

Secondly, I would like to point out that individual information is lost when an individual submits his input as aR1b or "I prefer a to b or I'm indifferent between a and b." The system does not know which, and this introduces ambiguity at the outset. Not only that, but say an individual is indifferent between a and b. He has two ways to express it! He can submit either aR1b or bR1a. The resulting analysis becomes meaningless as the system knows not how many of the individual aRb's represent indifferences and how many of them represent preferences. Ditto for the individual bRa's! There can be no meaningful social welfare function given these kinds of inputs.

Therefore, I suggest that Arrow's approach is not acceptable and that his conclusion that social choice is impossible is invalid. A more rigorous approach is necessary involving the possibility of ties between orderings as elements of the range. One possibility of dealing with these ties is to randomly choose among them which I think my friend, Ben, at Oxford is considering as a doctoral these.

For more on this subject, please see my website Social Choice and Beyond.

What I Learned from General Rosecrans

One of my distant relatives, William S. Rosecrans, was a General in the American Civil War. My Grandmother's maiden name was Rosenkrans, but one branch of the family changed the spelling of the name to "Rosecrans" supposedly so it "wouldn't sound so German." I found all this out from a book I got out of the UCSD library entitled something like "Rosecrans: The Edge of Glory." After graduating from West Point before the Civil War, Rosecrans became a General and a rival of Ulysses S. Grant. After not showing up for a battle where the two of them were supposed to fight together, Grant was criticized by Rosecrans and the two of them became lifelong enemies.

Rosecrans was ordered to go behind Confederate lines in Tennessee where the Confederates massed their troops against him. Rosecrans' requests for reinforcements and more supplies were ignored by a power structure that had taken sides in favor of Grant. Consequently, he got his butt kicked at the Battle of Chickamauga. What I learned from him though, which I think is one of life's most important lessons, is that as Rosecrans' options diminished, he always took the best option that was available at any point in time. I think this is what a rational person does. At any point one has a set of available options. This set is time-varying. The set may be augmented with better options or it may be diminished with the good options vanishing. The important thing is to always take the best option even as the available options are getting worse. This is precisely what Rosecrans did!

After he lost the Battle of Chickamauga, he was sent to the Boonies in Missouri or somewhere for the duration of the war, a sort of demotion, on orders signed by none other than U. S. Grant, his nemesis. After the war, Rosecrans moved to California where he had a 14,000 acre ranch in Redondo Beach. Still a major thoroughfare, Rosecrans Blvd. is now located in the heart of LA. Rosecrans was involved in various railroad and mining ventures in Mexico and elsewhere. He was twice elected to Congress. When U.S. Grant went broke after his term as President, Rosecrans rose from the floor of Congress to speak against providing him with a pension.

Garfield was Rosecrans' friend, and, when he was President and under other friendly Presidents, Rosecrans was named Ambassador to Mexico and Secretary of the Treasury. A military installation in San Diego was named Fort Rosecrans and Rosecrans Blvd. is still a major street in San Diego as well as LA. The U.S. Grant Hotel in San Diego was built by one of Grant's sons or grandsons so the Civil War presence of these two rivals exists side by side in this great city.

Rosecrans's various ventures were none too successful, and he cut a rather sad figure at Civil War reunions, apparently never having recovered from his loss at Chickamauga and criticism that was directed at him for leaving the field of battle, a fact that still is in dispute, although Rosecrans had his defenders as well as detractors. General Thomas, on the other hand, became known as the "Rock of Chickamauga" for holding his part of the line as the rest collapsed. I think the book was entitled "The Edge of Glory" since Rosecrans came so close to being the winning Civil War General. His skills were probably superior to Grant's. However, "politics" and Rosecrans' tendency to criticize his superiors combined to convey the glory on Grant not Rosecrans.

What does this have to do with Preferensism and Social Choice? The basis of these fields is the individual's forming a preference list over a set of options ranking his preferences from top to bottom or from first to last. It would seem fundamental that this set is time varying although this basic fact is the cause of Arrow proving that Social Choice is impossible. However, as I've said before, "the difficult we do right away, the impossible will take a little longer." For why I think Social Choice is possible, please see my website, Social Choice and Beyond.