[EM] Remember Toby

[Jameson Quinn]

I thought of a simpler way to explain my "safety" fix. The full system
description follows, with my new phrasing in bold.

N days before the election, all candidates (including declared write-in
candidates) rank order all other candidates (including declared write-in
candidates). These orderings are announced. In the election, all voters
submit an approval ballot, with two spaces for write-ins. Total approvals
and number of bullet votes are counted for each candidate and announced.
(Bullet votes are votes for only one candidate, including all valid or
invalid write-in votes.) Then each candidate may grant the number of bullet
votes they received to N other candidates from the top of their preference
list, where N can be any number including 0. All candidates decide what
number N to use simultaneously, and then those decisions are announced
publicly. *Take the two candidates with the highest approvals. Recount those
two as if they hadn't approved each other (that is, without adding any
bullet votes from one to the other).* The winner is the candidate *of those
two* with the highest approval in this final count.


The purpose of removing the mutual votes from the top two before deciding
the pairwise winner of these two is, as I explained before, to make it so
that one candidate will never lose because they approved another one. This
frees candidates to be honest in their approvals.

I believe that this system, as described, is pareto-dominant over plurality,
asset, and approval.

It is also very Condorcet-compliant. That is, assuming that X% of all
candidates' voters agree with their candidate's preference order, and that
the other (100-X)% have preferences which cancel each other out (random
noise); that this X is the same for all candidates; that all voters who do
not agree with their candidate do not bullet-vote (voting for a random
number of extra candidates), and all voters who do agree with their
candidate do bullet vote; and that there is a true pairwise champion; then
the pairwise champion will win in a (unique) strong Nash equilibrium. This
is a very solid result, which relies on the perfect information of the
candidates when choosing how to "delegate" their approvals; it is NOT true
of systems such as Approval or even DYN (without the preference-ordering and
top-two-pairwise-recount aspects). It is not even true of any Condorcet
system I know of (because of strategy)! So this system (and some obvious
variants) is in fact *the most Condorcet-compliant* system I know of.

Since it is also relatively simple to understand - not as simple as
approval, but not too far behind - I think it makes an excellent candidate
for a practical proposal.

Jameson Quinn


> I'd add my "safety" fix to the near-clone problem, *if* someone can think
> of an easy way to describe and motivate it. Basically, it looks at any
> candidate who mutually approve with the winner, and sees if they would beat
> the winner (pairwise) with those mutual approvals turned off. This helps
> when, for instance (honest preferences):
>
> 35: X1>X2
> 25: X2>X1
> 21: Y>>X2
> 19: Y>>X1
>
> If X1 and X2 approve each other, the right thing happens (X1 wins), no
> matter what Y voters do. If they do not, this fix does not attempt to read
> anyone's minds (or to ask people again in a runoff).
>
>
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