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

[fsimmons at pcc.edu]

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.

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.