[EM] Remembering the plain English

Kevin Venzke stepjak at yahoo.fr
Tue Jul 8 10:28:01 PDT 2003

John, or anyone,

Does Saari really think that voters, in Approval, would not use any
strategy?  Or is he just concerned about the zero-info cases?

I wonder if this will be of interest.  Mike Ossipoff on Approval strategy:

 --- "John B. Hodges" <jbhodges at usit.net> a écrit : 
> Greetings- It occurred to me this morning that a lot of Saari's 
> mathematical critique of Approval voting may be beside the point. 
> What is AV INTENDED to do? It (attempts to) pick the candidate that 
> the greatest number of people regard as not unacceptable.

That might be the "intention," but I think it's safe to say that Approval
supporters (as myself) expect a bit more out of it.

> Contrast this with Plurality, which (attempts to) pick the candidate 
> that the greatest number of people regard as the "best" candidate. Or 
> Borda Count, which (attempts to) pick the candidate who beats the 
> greatest number of other candidates in voters' individual rankings. 
> (Borda count assigns a number to each candidate equal to the number 
> of other candidates THAT candidate beats in THAT voter's ranking. 
> These numbers are then summed for each candidate across all voters.) 
> Or Condorcet-variation-x, which (attempts to) pick the candidate, if 
> there is one, that would beat each of the others in a two-person 
> contest.

Despite the different descriptions of what they are trying to do, I would
say that Approval, Condorcet, and Borda (with sincere voters and equal
candidate spacing) would likely elect similar candidates.

> Saari is making the point that a profile of voter's preferences, 
> described in terms of ordinal rankings of the candidates, will 
> usually not determine a unique winner under AV. Indeed in a wide 
> variety of such profiles, AV could generate ANY POSSIBLE result, 
> within the rules of AV, because AV gives the voters discretion to 
> mark their ballots in several equally-legitimate ways. This may be 
> true and may give you valuable insights into other properties of AV, 
> but the profiles of voter's preferences, expressed as ordinal 
> rankings, are strictly-speaking irrelevant to AV. To judge AV, you 
> need voter's sets of "acceptable" and "unacceptable" candidates. This 
> is not the same as their ordinal rankings, and cannot be derived from 
> them.

Granted, you can't divine an AV election's result knowing only relative
preferences. It would also help to know the perceived odds of each candidate
for each voter, the utilities, and the cutoffs, or strategy used.  When I make
statements about who would or wouldn't win an Approval election, I assume
that the voters are using the "Better-Than-Expectation" strategy (in Mike
Ossipoff's article).

> So, for example, The Approval-voting "nightmare" I quoted from Saari 
> yesterday: 9,999 voters rank the candidates ABC, 1 ranks them CBA, 
> all vote for their top two. B wins with 10,000 votes to A's 9,999. AV 
> is here doing exactly what it set out to do; this is not a 
> malfunction. I doubt any other voting method would do the same, but 
> that is not surprising, because they are trying to do other things.

I think this could be called a malfunction.  It's possible, I suppose, that
the AB|C voters are at least "okay" with both A and B, and are just being "honest"
in approving both of them.  But more likely, the AB|C voters have obtained some
quite flawed information about C being the guy they need to beat.

The other possibility is that this is a zero-info election, where it is
not known how viable anybody is.  Then the A>B>C voters should approve B if
B's utility exceeds the average utility of all three candidates.  The B
victory wouldn't really be a "malfunction" in that case.

Kevin Venzke
stepjak at yahoo.fr

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