3 ms·

The problem I have with this is that the score from 0 to 1 isn't tied to any strong foundation. Suppose that I rate a candidate 0.7, and my neighbor ranks the

by drdeca 9y ago

The problem I have with this is that the score from 0 to 1 isn't tied to any strong foundation. Suppose that I rate a candidate 0.7, and my neighbor ranks the candidate 0.6 . Does this mean that I like the candidate more than my neighbor does? What does that mean? How can we tell? Suppose you take two people who would vote in the same way, but then you take all the scores of one of the people, and square them. These are all still scores between 0 and 1, and so a valid way to vote, and it keeps the preference order in place. But what do the difference in these scores mean? "amount of happiness"? How could we quantify this? The way that seems to make the most sense to me is a normalized vNM utility. A person's least favorite candidate (or least favorite candidates if some tie for this position) get(s) the rating 0, and their favorite candidate(s) get(s) the score 1. All other candidates are scored as the probability r such that the voter is indifferent between that candidate, and (probability (1-r) of [least favorite candidate]) and (probability r of [most favorite candidate]). This gives a well defined foundation for what score a voter would give a candidate, a clear definition for what a 0.6 means vs a 0.7 . The system where you just pick the candidate with the highest average rating though, does not incentivize voting in this manner. I have an idea for a system which I think would incentivize voting this way, and which would optimize the expected value of a weighted sum of everyone's vNM utility. (it is a weighted sum because the utilities are normalized between 0 and 1, and different people's vNM utilities are incommensurate. The weighting is in the normalization. It is I think the most neutral weighting it can be.) However, it would probably be entirely impractical. The idea is this: Each person states their utility for each of the candidates listed, and the system makes sure that these utilities are normalized. Then, each voter gets 1 (arbitrarily subdivisible) point of voting probability. Then, a bunch of "trading" is automatically done, where say, as an example, if two people have different first picks, but would both prefer some other candidate as a close second, they could both give up some "undifferentiated" voting probability in exchange for some which is restricted in some way, based on whatever deal they made. All the deals would probably be made automatically, because it would just be so incredibly inconvenient otherwise, and also having the result be biased towards voters who are better at trading probably wouldn't be great. Once there are no more trades to be done, all the remaining undifferentiated voting probability goes to the voters' first choice. Then, the winner is chosen randomly, with the probability of winning corresponding to the proportion of the voting probability that was assigned to them in the end. Assuming an efficient market, this should optimize the expected value of a weighted sum of the voters' vNM utility (assuming rational voters). Unfortunately, it is rather complicated, and I think it would probably be too computationally intensive to run. Oh well.

Bromskloss 9y ago
> Suppose that I rate a candidate 0.7, and my neighbor ranks the candidate 0.6 . Does this mean that I like the candidate more than my neighbor does? What does that mean? How can we tell? Each voter should rationally vote in whatever way maximises the expected value of his utility of the outcome. The extent to which your vote "looks like your actual preferences" depends on how the voting system is designed.
- drdeca 9y ago
  Sure. My point was that the "pick the one with the highest average rating" doesn't obviously incentivize a particularly meaningful way to vote. I think that ideally, if it is possible without giving up too much, it is desirable that how a person would rationally vote doesn't depend very much on what they know about how other people will probably vote (though this probably isn't the most important consideration). If the system is based on people giving ratings, and there isn't anything that these ratings are designed to exactly mean, then it seems likely to me that the system wouldn't just so happen to be such that the way people are incentivized to vote would mostly not depend on how others are expected to, and also unlikely that the way people would rationally vote would match particularly well with the way that the designers of the voting system imagined. The system I gave was intended to be one in which the way people would be incentivized to vote would correspond to their preferences in a clearly defined (and sensible) way.

by drdeca 9y ago

Bromskloss 9y ago

> Suppose that I rate a candidate 0.7, and my neighbor ranks the candidate 0.6 . Does this mean that I like the candidate more than my neighbor does? What does that mean? How can we tell? Each voter should rationally vote in whatever way maximises the expected value of his utility of the outcome. The extent to which your vote "looks like your actual preferences" depends on how the voting system is designed.

drdeca 9y ago
Sure. My point was that the "pick the one with the highest average rating" doesn't obviously incentivize a particularly meaningful way to vote. I think that ideally, if it is possible without giving up too much, it is desirable that how a person would rationally vote doesn't depend very much on what they know about how other people will probably vote (though this probably isn't the most important consideration). If the system is based on people giving ratings, and there isn't anything that these ratings are designed to exactly mean, then it seems likely to me that the system wouldn't just so happen to be such that the way people are incentivized to vote would mostly not depend on how others are expected to, and also unlikely that the way people would rationally vote would match particularly well with the way that the designers of the voting system imagined. The system I gave was intended to be one in which the way people would be incentivized to vote would correspond to their preferences in a clearly defined (and sensible) way.