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

[fsimmons at pcc.edu]

After Kevin's and Kristopher's comments, which I agree with, I am hesitant to beat a dead horse, but I 
have two more things for the record that should not be overlooked:

First, just as there are deterministic voting methods that elicit sincere ordinal ballots under zero 
information conditions, there are deterministic methods that elicit precise sincere utilities under zero 
information conditions.

An example, due to Samuel Merrill (of  Brams, Fishburn, and Merrill fame), simply normalizes the 
scores on each range ballot the same way that we convert a garden variety normal random variable into 
a standard one: i.e. on each ballot subtract the mean (of scores on that ballot) and divide by the 
standard deviation (of scores on that ballot).  Once each ballot has been normalized in this way, elect 
the candidate with the greatest total of normalized scores (over all ballots).

Second, I want to get at the heart of the incommensurability complaint: in most elections some voters 
will have a much greater stake in the outcome than others.  For some it may be a life or death issue; if X 
is elected your friend's death sentence is commuted, if Y is elected he goes to the chair.  Other voters 
may have only a mild interest in the outcome.

How can this problem of incommensurability of stakes be addressed by election methods?

Answer: it cannot be addressed by any method that satisfies the basic requirements of neutrality, 
anonymity, secret ballot, one-person-one-vote, etc.  

So this "failure" to provide for stark differences in stakes is not unique to Range.  It applies to all decent 
voting methods.

Having said that, Range has an option that is better than most methods that are based on ordinal 
ballots:  give top rating to all candidates that might pardon or commute your friend's death sentence, and 
give bottom rating to all recent former governors of Texas and their ilk.

----- Original Message -----
From: Kristofer Munsterhjelm 
Date: Thursday, August 25, 2011 7:38 am
Subject: Re: [EM] the "meaning" of a vote (or lack thereof)
To: fsimmons at pcc.edu
Cc: election-methods at lists.electorama.com

> fsimmons at pcc.edu wrote:
> > Here's a link to Jobst's definitive posting on individual and social
> > utility:
> > 
> > http://lists.electorama.com/htdig.cgi/election-methods-
> electorama.com/2007-February/019631.html
> > 
> > 
> > Also, I would like to make another comment in support of Warren's
> > thesis that cardinal range scores are as meaningful or more so than
> > ordinal rankings:
> > 
> > Consider that Borda is a method based on rankings. Do the rankings
> > in Borda have the same meaning to the voter as the rankings in IRV
> > do? From Arrow's point of view they do; the ballots are 
> identical in
> > format, and in either case (for a sincere vote) you simply 
> rank A
> > ahead of B if you prefer A over B.
> > 
> > But now let's compare Borda with Range; Suppose that there 
> are ten
> > candidates and that the Range ballots ask you to rate them on 
> a scale
> > of zero to nine. On the Borda ballot you are asked to rank 
> them from
> > one to 10.
> > 
> > Borda elects the candidate with the "highest" average rank 
> (i.e. the
> > lowest average rank number). Range elects the candidate with the
> > highest average range score.
> > 
> > Now, tell me why Arrow worries about the supposed incommensurable
> > ratings on a scale of zero to 9, but sees no problem with the 
> one to
> > ten ranking scale?
> 
> Doesn't that confuse the meaning of ranking (versus rating) in 
> itself 
> with the meaning of ranking, as interpreted by the system? I 
> could make 
> a ranked ballot system like IRV that would produce non-monotone 
> results 
> given the ranked ballots that are input to it -- but I could 
> also make a 
> rated ballot system, say "the winner is the candidate with the 
> greatest 
> mode", that would also give non-monotone results (since if X is 
> the 
> candidate with greatest mode, rating X higher may lower his mode).
> 
> Thus, if ratings and rankings are to have meaning, it would seem 
> that 
> this meaning would be independent of the system in question. 
> Otherwise, 
> the meaning would have to be considered with respect to the 
> space of 
> possible voting methods that could use the ballot type in 
> question, and 
> there would be very many outright weird voting methods on both 
> ballot types.
> 
> If, then, meaning is independent of the method, then Borda's 
> internal 
> workings (where it assigns a score to each ranking) doesn't mean 
> that 
> Borda makes use of a rated ballot, but simply that Borda acts 
> *as if* 
> the ranked ballot is a rated ballot. Because of this, it may 
> produce 
> counterintuitive outcomes (e.g. failing the majority criterion). 
> For 
> that matter, we know that every ranked ballot method can produce 
> a 
> counterintuitive outcome (if we consider determinism, unanimity, 
> non-dictatorship, and IIA intuitive). However, in the 
> independent-of-method point of view, that doesn't make the 
> ranked ballot 
> itself ill-defined.
> 
> To use an analogy, say you could instruct a robot either by 
> giving 
> somewhat general commands (ranking), or by explicitly 
> programming it 
> (rating). Now, if you were to find a theorem that there's no way 
> to 
> construct the robot so that it never misunderstands any of your 
> commands, then that doesn't mean that the concept of a general 
> command 
> is without meaning. It just means that there are hard limits to 
> the 
> robot's understanding.
> 
> Of course, one could then argue what the meaning of a ranked 
> ballot is. 
> I think this is easy enough: a ranked ballot is a compact 
> representation 
> of a combination of preferences (prefers A to B, B to C, C to D, 
> etc), 
> so that the combination is transitive.
> (Using that definition, one could even design a "strategy-free" 
> method 
> where voters are encouraged to submit full rank orders as 
> defined: the 
> method would be random dictator but with a pre-stage that 
> removes a 
> random subset of the candidates. That method would be 
> nondeterministic 
> and not that good in practice, though.)
> 
>