[EM] Strategic Voting and Simulating It

[Raph Frank]

On 10/14/08, Greg Nisbet <gregory.nisbet at gmail.com> wrote:
> I would like to know what is currently wrong with the strategic voting
> simulations.

One objection I would have is that in real life all candidates are not
treated equally by the voters.

This is especially true in something like plurality.  One of the 2
main party candidates is certain to win.  In effect, the initial state
of the process doesn't start with a blank slate, the 2 party
candidates start ahead of everyone else.

Your strategy method is independent and it treats all candidates
equal, while in RL, that is not the case.

I would suggest the following:

1) Pick 2 candidates as the 'top 2'

2) Each voter votes as if the top 2 are the only candidates
- most methods handle this as a pure majority based method

3) Loop through each voter one at a time
- Test all possible votes that voter can pick
- Pick the one that gives the best result for the voter

4) goto 3, until stability is achieved (or a max number of passes occurs)

The trick is how you calculate the best result.

My opinion is that "Best result" should give priority to the winning
margin of the first and second place candidate and then works
downwards to less important margins.

So, taking plurality as an example, if my ratings are

A: 100
B: 00
C: 30

and the results are

A: 0
B: 44
C: 55

If I vote for A, the results become

A: 1
B: 44
C: 55

This gives a winning margin of C>B by 11
If I vote for B, it gives a margin of C>B by 10
If I vote for C, it gives a margin of C>B by 12

Thus, my optimal vote is to vote for C and not for my favourite A.

You can then move on to the next voter and repeat.

The result is that every voter votes for one of the top 2 and this
matches what happens in real life.

However, if I was to use approval, then it is different.

Option 1:
If I approve only C, the result is

A: 0
B: 44
C: 56

This gives
C beats B by 12 (highest priority)
B beats A by 44

Option 2:
If I approve C+A, then the result is

A: 1
B: 44
C: 56

C beats B by 12 (highest priority)
B beats A by 43

Option 1 and option 2 tie for the highest priority margin, so the next
highest margin kicks in.

This gives option 2 a slight edge, so I approve both C and A.

I think this method better reflects what actually happens in RL and
the effect of polling.  People have to decide how to vote based only
on the effect of their personal vote.

Hopefully, in RL, if the election was an approval election, then
polling companies would collect approval based polls.

I think it should work for any method, with reasonable definitions of
margins of victory.

Condorcet could arrange the candidates in order.  The margin of
victory between the first and 2nd candidate would be the first margin
and so on.

In IRV, the 'margins' could be the number of votes held by the
eliminated candidate relative to the lowest candidate who isn't
eliminated.  The first margin would thus be the margin of victory in
the final round, and work backwards.

An added feature is that it can be used to measure how susceptible a
method is to duverger's law.  With random voters and candidates, the
winning candidate should be random.  However, if the 2 candidates who
are marked 'top 2' at the start have a much higher chance of winning,
then the method can be deemed to be susceptible to duverger's law.
Also, it gives a measure of how susceptible a method is.

It could be defined as

F = fraction of times one of the 'top 2' wins
C = number of candidates

Susceptiblity to DL = (F - 2/C)/(1 - 2/C)

If it is random, one of them will win 2/C of the time, so the above
gives 0, which means not susceptible.

If one of them wins all the time, then F = 1, so the above formula
gives a value of 1, which means completely susceptible.

I think plurality will manage an F=1 score and others would have a
much lower score.  It would be interesting to see what IRV scores.

Ofc, it assumes that top-2 status is a gift from the Gods, which isn't
totally true either.