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

Tue Aug 23 13:47:12 PDT 2011

On Aug 21, 2011, at 5:06 PM, Warren Smith wrote:

> Kenneth Arrow has worried that range-voting-type "score" votes might have no or
> unclear-to-Arrow "meaning."  In contrast, he considers rank-ordering-style
> votes to have a clear meaning.
> Nic Tideman has also expressed similar worries in email, but now about
> the "lack of meaning" of an approval-style vote.
> In contrast, I think Tideman regards a plurality-style "name one
> candidate then shut up"
> vote as having a clear meaning.
> 
> E.g. "what does a score of 6.5 mean, as opposed to a score of 6.1, on
> some ballot?"
> 
> But the Bayesian view is: whether or not Arrow or Tideman or somebody
> has a more-or-less muddled mental notion of the "meaning" of a ballot,
> is irrelevant.   The only genuinely meaningful thing is "who won the
> election?"
> All meaning of any ballot therefore derives purely from the rules
> for mathematically obtaining the election-winner from the ballots.

Arrow would not, I think, quarrel with the claim that a cardinal ballot has a pragmatic/operational "meaning" as a function of its use in determining a winner. 

But but it's an unwarranted leap from that claim to use the ballot scores as a measure of utility. Arrows objection to cardinal scores, or one of them, is that they are not and cannot be commensurable across voters.

> 
> For a simple example of how ballots have no inherent meaning without
> voting system rules, consider plurality and AntiPlurality voting in which
> the meanings of a  "name one candidate" ballot are pretty much opposite
> (plurality: most-named candidate wins;
> AntiPlurality: least-named candidate wins).
> 
> Let us now enquire more deeply about ballot "meaning."  In a non-monotone voting
> system like Instant Runoff,  your vote A>B>C can cause A to lose, whereas
> your vote B>C>A would have caused A to win.   Would Arrow be right if
> he said IRV is wonderful
> because "A>B>C" has a "clear meaning"?  Or would a Bayesian be right
> in saying this
> example indicates the "meaning" Arrow had in mind, was not valid?  Indeed the
> Gibbard-Satterthwaite theorem
>   http://rangevoting.org/GibbSat.html
> shows that in essentially ANY rank-order ballot system and also in the
> plurality and
> AntiPlurality systems with "name one candidate" ballots -- i.e. exactly
> the systems Arrow & Tideman thinks "have meaning" -- there ALWAYS
> exist elections
> in which some voter's vote of A>B>C will cause a worse election winner
> (for the A>B>C
> notion of "better" and "worse") than some different
> dishonestly-ordered vote would
> have caused.  (And with Plurality and AntiPlurality, "dishonestly" ranking
> your non-favorite candidate top or your really-not-worst candidate
> bottom, can be the only way
> for you to get an improved election result.)
> In such an election, what is the "clear meaning" of an A>B>C rank-order vote?
> 
> Gibbard identified/invented exactly two rank-order ballot systems in
> which honest and strategic
> voting were the same thing (this required him to employ
> non-determinism), but stated
> that both of his systems were not good enough for practical use since they
> "leave too much to chance."
> 
> In contrast, consider the "double range voting" system invented by
> F.Simmons and Warren D. Smith
>   http://rangevoting.org/PuzzRevealU2.html
> 
> This system (or others of the Simmons class) ARE good enough for
> practical use if any
> rank-order system is (since it leaves only an arbitrarily small amount
> of the deciding to chance,
> and deviates from your favorite system in an arbitrarily small way).
> 
> In this voting system, each ballot contains a part on which the voter
> is urged to
> provide her honest scores (on, say, an 0-to-9 range) for each
> candidate.  In this system,
> ONLY voting on this ballot portion in a unique honest manner is strategically
> best.  Any deviation from perfect honesty (or omision of information)
> is a strictly worse voting strategy.
>   That is, if your expected utility if A wins is 6.5 and your
> expected utility for B
> winning is 6.1 on an 0-to-9 scale (defining the utility scale so
> you've rated the
> best available candidate 9 and the worst 0)
> then you MUST score A=6.5 and B=6.1 EXACTLY, otherwise you are guaranteed
> to get in expectation a worse-utility election result.
> 
> So contrary to assertions by the likes of Arrow that utility is "unmeasurable"
> or that range votes "lack meaning" it seems to me that we have a very
> clear, totally unique,
> not changeable by one iota, meaning for the scores 6.5 and 6.1 deriving
> wholy from the procedure the voting system uses to determine the
> winner from the votes.
> This is wholy unlike EVERY allegedly-practical rank-order voting system.
> 
> So Arrow, and Tideman (and anybody else) are simply wrong if they
> assert scoring-style votes
> are inherently less-meaningful than rank-ordering-style or
> name-one-candiate-style votes.
> 
> So now Arrow might perhaps riposte that to HIM, deep in the recesses
> of his brain,
> rank-order votes have more meaning, even though every voting system he
> and his colleagues have ever considered for practical
> use, disagrees with his private meaning in at least some situations,
> and even though (therefore)
> the true meaning of your vote really also depends on how the OTHER
> voters are voting, not just
> on the candidates and your evaluation of them in your private brain.
> (I would have to then counter-riposte: who cares?)
> 
> Another riposte might be that under the assumption there are a large number
> of other voters all of whom vote TOTALLY RANDOMLY and independently,
> your vote can have a clear meaning, and in some rank-order systems (e.g. Borda)
> this meaning coincides with "honest ordering."
> I would then riposte that (a) that assumption is false, and (b) under
> the same assumption
> approval voting also has a "clear meaning" (namely: you should
> "approve" candidates
> above mean utility for you).
> 
> Does our argument tell us that score-style votes inherently have MORE meaning
> than rank-order style votes?  (Exactly contrary to Arrow?!?)  Well... not
> necessarily.   Yes, score-style votes certainly inherently convey more
> information
> than rank-ordering-style votes (strengths of preference as well as preferences).
> And I would claim that if they were employed for the honest-part of
> double range voting
> ballots, they inherently have more meaning.  But if employed for plain
> range voting, then it is posible
> to construct 4-candidate election situations in which it is strategically best
> for a range voter to misorder, so we run into the same
> Gibbard-Satterthwaite-style issues (albeit only with 4, not 3, candidates).
> 
> All this analysis really tells us is the Bayesian view is correct.
> And certainly that any dismissal
> of range- or approval-style voting on the grounds of their claimed
> "inherent lack of meaning",
> is hogwash.
> 
> -- 
> Warren D. Smith
> http://RangeVoting.org  <-- add your endorsement (by clicking
> "endorse" as 1st step)
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