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

fsimmons at pcc.edu fsimmons at pcc.edu
Wed Aug 24 19:30:16 PDT 2011

```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?

Note that in this case a scoring challenged voter could rank the candidates, and then subtract their
respective ranks from 10 to get evenly spaced range scores on the required scale.

Thus 1 , 2, 3, 4, ... 9, 10 transform to 9, 8, 7, 6, ... 1, 0, respectively.  [When Borda is counted, this
transformation is part of the counting process; Borda elects the candidate with the largest Borda score.]

If the scoring challenged voter doesn't like the evenly spaced aspect, there is nothing she can do about it
in the ranking context, but in the range context she can adjust some of the ratings to reflect bigger and
smaller gaps in preference.

> 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.
>
>

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