In his book Social Choice and Individual Values Arrow supposedly proves that it is impossible to take a group of individual preference profiles and amalgamate them to form a social preference profile or social choice. Each individual profile would consist of the ordering of, for instance, 10 alternatives in order of preference from first to last, and the social profile would consist of the same alternatives in some order from first to last. Of course, the number of alternatives is arbitrary. Now first of all this is an artifical problem. In the real world voting situation we would be concerned about selecting one winner given individual preference profiles as inputs - not an ordering. In the economic problem, we would be concerned about assigning individual outcomes given individual preference profiles where each item to be ranked would consist of a work - consumption bundle. That is each preference would be an amount an individual would be willing to work in exchange for that bundle of consumption items indicated in that preference. In general most individuals would probably want to work less and consume more and that would be indicated in their ranking of various work - consumption bundles.
Well, neither of these situations represent the model that Arrow used to prove social choice is impossible. Secondly, any actual social choice rule had to meet Arrow's 5 Conditions at least one of which is completely arbitrary. Anyone could set up their own group of conditions and demand that a rational social choice rule must meet them. The suspect condition is Condition 3 - Independence of Irrelevant Alternatives. Basically this demands that, if there were 10 candidates, for instance, and 100 voters, and the voters all ranked the candidates in order of preference, and then one candidate died, the social choice rule should be able to cross out the dead candidate's name in each individual list and the result would be the same as if you crossed out the dead candidate's name in the original social choice profile. Of course, if everyone just revoted on the new candidate list, this problem would cease to exist.
And actually this is what we propose in preferensism: a continual revoting. Let me say right off the bat that this wouldn't be possible without the technology of computers we have today in the year 2006. I assume that everyone has access to a PC and a secure account, and then the data is processed by a centralized computer to come up with the social choice. For instance, let's consider the economic situation. Everyone inputs their data consisting of work and consumption preferences. Now we assume that each individual can change his or her mind as often as he or she wishes. That is data inputs can vary in real time. Some individuals might change their input on a daily basis. Others might be satisfied with the same input for a lengthy period of time. At each instant, the centralized computer (the one that is figuring out the social choice which consists of work assignments and consumption bundles for all individuals) comes up with a social choice which maximizes utility or "happiness" based on giving each individual as close to his first preference as possible while considering each individual equally. That is no one gets special consideration in determining the social outcome. For this scenario, Arrow's Impossibility Theorem is entirely irrelevant. Why? Because there are never any irrelevant alternatives. Why? because there is a continual revoting, and, by definition, you can only have an irrelevant alternative when some alternative has been eliminated from the alternative set and then the social choice is made with the original individual input data but with a changed alternative set.
Another thing to consider is that each individual does not even know the full set of alternatives because each individual is concerned only with his or her individual work-consumption preferences and not his or her neighbor's. So the central computer has to take all this data and integrate it not only in a coherent way (the totality of work assignments produce all the requisite consumption bundles) but also in a way as to maximize utility. Is this fair? Yes, because each individual's input is given the same consideration. Furthermore, if there are more ways than one to maximize utility, preferensism picks the one that reduces a measure of inequality over the whole society.
Therefore the central computer takes the individual inputs, considers all possible work assignments and corresponding consumption bundles, figures the social utility for each assigment based on how close to first preference each individual achieves and then chooses that set of assigments that maximizes social utility and with that constraint minimizes inequality. For instance, if there are 11 alternatives and an individual gets his first choice, we could say his individual utility is 1. If he gets assigned his last place preference we could say his utility is 0. Second place would be an individual utility of 0.9 etc. The central computer would seek to maximize utility over all individuals or for society as a whole. In this scheme could someone end up very dissatisfied? Yes, if he or she were assigned an outcome which represented his or her last choice or a choice near the last choice. It's a logical possibility. In practice, as long as there is a large set of available alternatives, it should be possible to work things out so that everyone gets close to the top end of his or her preference list.
For more on this please see my website Social Choice and Beyond
