[EM] 12/30/02 - Alex, Irving still holds the Trump Card:

[Alex Small]

(First, let it be pointed out that Donald has engaged us in debate here by
responding to a response.  He was criticized for failing to do that.)

So, basically, you argue this:

In an Approval election, voters will respond to polling information by
voting for their favorite of the top 2 plus whomever they prefer to their
favorite of the top 2.  This is not a stunning insight for us.  Brans and
Fishburn argued the same more than 2 decades ago.

However, I do concede that widespread bullet-voting will not be equivalent
to plurality in most cases.  See?  We agree on something!

Anyway, to the extent that Approval is like IRV (I will point out a few
key differences momentarily) then Approval basically offers IRV without
the expense of implementing ranked ballots.

However, I see 3 key differences:

1)  The top 2 candidates in a poll may not be the 2 candidates who are the
first choices of the greatest number of people, as people can also vote
for lower choices.  Although the implications of that fact require some
amount of work, the conclusions drawn by many workers seem to be that this
increases the likelihood of the Condorcet Winner (when such a candidate
exists) being in the top 2.

The easiest way to illustrate this conclusion is with the classic example

40 Left>Center>Right
11 Center>Left>Right
 9 Center>Right>Left
40 Right>Center>Left

If enough people on the left and right (for reasons that may be either
pity or pragmatism) also indicate support of Center in a poll then he will
be one of the top 2 candidates and will most likely win the Approval
election.

Now, you may claim that the support for Center comes from "Pity Votes",
but perhaps it comes from a fear that their least favorite will win. 
People deciding to do whatever possibility to defeat their least favorite
are NOT giving "pity votes."  They're giving "Please help me!" votes.  In
other words, they're acting in their _own_ best interests, not the best
interests of a candidate.

2)  To continue with the above example, suppose that in an initial poll
votes only indicate support for their favorite.  Left and Right come out
on top.  It seems that Left will win after the centrists also give support
to their second choice.  A second poll will soon bring this out.

However, seeing a victory for Left, supporters of Right may decide to
support Center as well.  They're following a different version of the
above assumption:  In response to a poll, voters will vote for their
favorite of the top 2 as well as all candidates whom they prefer to their
favorite, AND POSSIBLY ANY CANDIDATES WHOM THEY RANK BETWEEN THEIR
FAVORITE OF THE TOP 2 AND THEIR LEAST FAVORITE OF THE TOP 2.

The key is that voters are acting defensively.  People on the Right are
saying "Well, might as well support Center, because he is better than Left
and right now Left is beating Right."  This is NOT pity!  This is
self-defense.



It's difficult to gauge how likely the phenomena in points 1 and 2 are. 
However, they are very real possibilities.  They cannot be predicted from
principles, but they can occur in response to the will of the electorate.


Finally...
3) Consider a true 3-way race, in which a poll gives 3 candidates levels
of support that differ by less than the statistical margin of error.  Here
it is difficult to predict what will happen.  Most people here argue that
voters will act to maximize their expected utility in the face of a true
3-way race.  If that indeed is true then the winner will be the candidate
with the greatest overall social utility.  Not a bad result, and certainly
not a "pity" result.

It's also hard to predict the outcome of an IRV election when 3 candidates
have roughly equal levels of first-place support in polls (obviously the
outcome can be determined from actual ballots, but I'm talking about
polls, which have margins of error).  A candidate's first instinct would
be to seek more first-place support.  However, if he draws too much
first-place support from the only candidate whom he can beat pairwise then
it will backfire, and he'll wind up in a race against somebody whom he
can't beat.  So, he must decide very carefully where to try and poach more
support.

By contrast, in a true 3-way race with Approval, it doesn't matter where a
candidate draws more support from in a campaign.  It only matters that he
gets more votes.  In that sense, Approval makes campaign strategy more
straight-forward than IRV, since Approval says "Persuade more people that
you deserve a vote" (merit, not pity) while IRV says "Be careful not to
draw so much support that you knock out the person whom you can beat."


So, in summary:

1)  In many cases IRV and Approval will function in the same manner.  In
those cases, Approval offers IRV without the added expense of new voting
machines.

2)  When lower choices play a significant role in an Approval election
it's because voters are defending their own interests.  They are
supporting any and all candidates whom they prefer to a likely winner. 
Those votes for lower choices are based on an assessment of relative
merit, not "pity".

3)  In a true 3-way contest, Approval offers more transparency for
candidates and voters.  The consequence of seeking more support from a
faction is more support, not the possibility of knocking out a soft rival.
 Likewise, the consequence of voting for a candidate is that he receives
more votes, not that he will a "soft target" has been eliminated.



Seen in this light, Approval offers voters a way to defend their best
interests in a rational manner.  Pity plays no role here.




Alex


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