[EM] Arrow's Theorem - The Return (again)

[John B. Hodges]

>  >Date: Sat, 2 Aug 2003 13:17:36 -0700 (PDT)
>>Subject: Re: [EM] Arrow's Theorem - The Return (again)
>>From: "Alex Small" <asmall at physics.ucsb.edu>
>>
>>(snip much)
>>
>>Here's a good argument for why Approval flunks IIAC:
>>
>>Say that the electorate is as follows:
>>
>>30 (A>B)>C
>>30 (C)>A>B
>>40 (B)>A>C
>>
>>The parentheses indicate which candidates a particular group of voters
>>approved.  In this case, B wins with 70 votes.
>>
>>Now give all of the voters a ballot again, but don't include candidate C
>>on it.  If the people who approved both A and B the first time around are
>>rational they will only approve A this time.  If the people who only
>>approved C the first time around are rational they will only approve A
>  >this time.  A now wins 60-40.
>................
>John B. Hodges said:
>>  Alex's example above shows the possibility of a "spoiler effect",  i.e.
>>  in a two-person race between A and B, A wins, but adding C to  the race
>>  gives the victory to B. Those who vote for C give the
>>  election to their last choice, so if they understood the situation in
>>  advance, they would abstain from voting for their first choice.
>
>Alex:
>No.  There is never a disincentive to abstain from approving your first
>choice if you use approval voting.  Those who voted for C decided NOT to
>approve their second choice as well.  Maybe they had inadequate polling
>data and didn't realize what would happen if they abstained.  Maybe they
>wanted to punish A for not being good enough.  That is their right, and I
>will not criticize people who withhold votes from candidates whom they
>find to be unworthy.

(JBH) By hypothetically varying the approval thresholds of the 
voters, with the above set of preference rankings, you could give the 
victory to either A or B. If you like the result, praise the method; 
if you don't, damn the "bad strategy".

You make a good point, that polling data would show B as the 
front-runner, and by the strategy "Approve everyone you like better 
than the front-runner, and if you like the front-runner better than 
number two, approve them as well" A would win even with C in the 
race. C voters would not abstain from voting for their first choice, 
they would vote for their first and second. This illustrates Saari's 
point that the method is indeterminate; the performance depends on 
the voters following good strategy.

>Alex:
>I normally think of the spoiler effect as happening when the addition of a
>new candidate changes the outcome without the new candidate winning, and
>all voters voting sincerely.  In that case, any system that flunks IIA has
>the potential for a spoiler effect.  However, it's much less severe in
>approval because well-informed voters can make sure there is no
>"spoiling."  It's only if they follow sincere but uninformed information
>that they get "spoilage."

The more (reliable) information the voters have, the better their 
strategy can be. We don't know how bad this would be in practice, 
because Approval has not yet been tried on a large scale. I've heard 
that some professional societies use it; do they run straw polls 
before the actual vote? Advocates should make it clear that advance 
polling is important to the quality of the results.

-- 
----------------------------------
John B. Hodges, jbhodges@  @usit.net
Do Justice, Love Mercy, and Be Irreverent.