[Election-Methods] Improved Approval Runoff

[Peter Barath]

>47: Bush >> Gore > Nader
>27: Gore > Nader >> Bush (honest); Gore >> Nader > Bush (strategic)
>26: Nader > Gore >> Buch (honest);  Nader >> Gore > Bush (strategic)

>Bush wins the first rount, but loses for Gore in a runoff (IAR).
>With strategic voting, the spoiler effect is possible under simple
>approval.

But this example was made possible only by the fact that
many voters made bad estimates.

It's a well accepted fact that in the most cases (no, not
in all cases, as Warren D. Smith has low probability
counter-examples for that) a strategic Approval vote is made by:

- making a honest preference order
- putting a cutoff mark between the two candidates with the best
  chances
- if the better one seems to have more chance, put the cutoff
  immediately under her/him/it
- if the worse one seems to have more chance, put the cutoff
  immediately above her/him/it

But rarely is the question asked: what do we mean by the "two
candidates with the best chances"? I think we are best to measure
this only by the fact of how we expect all other voters to vote.

Which means that the concept of "two candidates with the best chances"
depends not solely on the candidates themselves but theoretically
possibly on the voting method too!

In your example with 47 percent firm Bush supporters the voters
were very wrong in supposing that he is a harmless candidate.
In reality, in this case the strategic votes would be identical
to the honest ones.

However, I think your example did point to a widely ignored fact:
that the ugly dilemma of the Plurality vote: "how will other
voters vote?" does exist in Approval, even if it's smaller.

So it's plausible to mix Approval. My favourite (at this moment)
is a preference ranking with an approval cutoff. For me it's
interesting enough that it can be used in two ways:

1. If there is a Condorcet-winner she/he/it wins. If there is
   not, the Approval winner wins.

2. Calculate the two candidates with the most Approval points
   and the pairwise winner of them wins.

Peter Barath

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