[EM] Anyone got a good analysis on limitations of approval and range voting?

[Raph Frank]

On Sat, Nov 7, 2009 at 8:12 PM, Matthew Welland <matt at kiatoa.com> wrote:
> It seems to me that approval and range voting eliminate most of the
> strategic opportunity in single winner elections and the marginal
> improvement of other methods is fairly small.

The recommended strategy in approval is to approve one of the top 2
and also any other candidates who are above your approval threshold.

The threshold is not so important, as it is likely that one of the top
2 will win, so that approval is the only one that matters.

You should approve all you prefer to the best of the top 2 and should
never approve someone you like less than the worst of the top-2.

Some possible thresholds

- approve all you prefer to the expected winner
- approve all you prefer to the expected utility of the election
- approve all you prefer to the best of the top 2
- approve all you prefer to the worst of the top 2

I prefer to the first first one as it will results in the condorcet
winner winning the election if there are accurate polls.

As long as voters know who are the contenders, then approval strategy
is pretty easy.

Where there are 3 contenders, there is still some issue with regard to
handling the middle candidate.  The voter would need to make a call
about which tie was more likely and also the differences in utility.

Also, strategy isn't necessarily a bad thing.

The problem with plurality is that it converges on the 2 party system.

It is a Nash equilibrium.

If you could go through each voter after an election and ask them if
they want to change their vote, most of them wouldn't.

It would normally just reduce the margin or victory for their
favourite of the top-2.

However, with approval, you can have a sequence that goes like:

A and B are the top 2, but C is the condorcet winning candidate.

Voters follow the policy that they will approve one of the top 2 and
any candidate they prefer to the expected winner.

Since every voter will only vote for one of A and B (since they are
the top-2), one of them must end up with less than 50% of the vote.

C is the condorcet winner, so he is preferred to whoever is the
expected winner by at least half of the voters.

Thus the first poll will show something like

A: 45
B: 55
C: 51

Thus C will suddenly be one of the top-2.

This might take a few polls, but as C gets more press reports, his
percentage will increase.

Once he is one of the top-2, he cannot be displaced.  No matter who is
the other one, he will be preferred to that candidate by more than
50%.

Also, once he is one of the top 2, any voters who prefer him to all
other candidates will suddenly stop approving either of A or B.  Thus
one of them will drop in popularity.


The point is that it isn't strategy that is the problem.  It is that
strategy results in the voters ending up with the the better of 2
evils.

With approval, the result is that a condorcet winner should normally
win, so any strategy results in a fair result.