[EM] the "meaning" of a vote (or lack thereof)

[Jonathan Lundell]

On Aug 23, 2011, at 4:07 PM, fsimmons at pcc.edu wrote:

> It seems to me that Arrow must want a unique generic meaning that people can relate to independent of 
> the voting system.  Perhaps he is right that ordinal information fits that criterion slightly better than 
> cardinal information, but as Warren says, what really matters is the operational meaning.
> 
> But back to a possible generic meaning of a score or cardinal rating:  if you think that candidate X would 
> vote like you on a random issue with probability p percent, then you could give candidate X a score that 
> is p percent of the way between the lowest and highest possible range values.
> 
> Note that this meaning is commensurable across the electorate.

So would a score that reflects the difference in height between each candidate and the voter, but neither one is a plausible utility measure. And that's assuming that a voter actually knew not only what the candidate would be voting on, but in each case how he would vote. That in itself is a judgement that each voter (even voters with the same preferences) would make differently. Worse, each projected vote would have to be weighted by some (incommensurable) sense of how important each vote is to the voter (the utility of each vote).

So now we've exploded the problem is coming up with a candidate utility to adding up a bunch of utilities of votes that we're guessing about years into the future. That seems worse than circular.

And *that's* assuming that the list of votes is the utility measure we want. But that's not really plausible, either. Consider as an extreme case voting for US President, though something similar obtains for legislative candidates with respect to leadership, initiative, ability to persuade others, &c.

But set that aside, and return to my first point. You don't help the problem of candidate utility by converting it to a sum of vote utilities.

> 
> Furthermore, with regard to commensurability of range scores, think of the example that Warren gave in 
> which the optimum strategy is sincere range strategy; in that example it makes no difference (except for 
> ease of counting) whether or not each voter uses a different range; some could use zero to 100, some 
> negative 64 to positive 64, etc.  A ballot will distinguish among the two finalist lotteries in the same way 
> after any affine transformation of the scores.
> 
> A few years ago Jobst gave a rather definitive discussion of this issue.  His investigation led to the result 
> that ideally the scores should allow infinitesimals of various orders along with the standard real values 
> that we are used to.  Jobst is skeptical about generic objective meaning for "utilities," but in the context 
> of voting, especially "lottery" methods, he can give you a precise objective meaning of the scores.
> 
> For example, if you have a choice between alternative X or a coin toss to decide between Y and Z, and 
> you don't care one whit whether or not X is chosen or the the coin toss decides between Y and Z, then 
> (for you)objectively X has a utility value half way between Y and Z. 
> 
> A sequence of questions of this nature can help you rationally assign scores to a set of alternatives.
> 
> I'll see if I can locate Jobst's results in the archives.