[EM] SARA as an example of a new class of voting systems

[Jameson Quinn]

Consider the class of voting systems where your vote for each candidate is
a real number from some set of possible numbers, and the voting rule is:
first eliminate the candidates with a median below some threshold, as long
as there are any above that threshold, and then use range totals among the
remaining candidates.

Optimal strategy will probably be to vote top, just above the cutoff, or
bottom. Since all strategic votes below cutoff will be at bottom, it makes
little sense to put the cutoff anywhere but epsilon above the bottom.

SARA is an example of that class, where the numbers you can give are 2, 1,
0, and -1e-20 (that is, -0.00000000000000000001), and the median threshold
is -0.5e-21. So, in SARA, the "accept" vote (1 pt) is probably almost never
strategically optimal; but when it's useful, it's useful for the wings to
help the center in a center squeeze situation, and in that situation there
are by construction over twice as many voters who could potentially give
the squeezed CW a 1 as there are voters honestly giving them a 2, so the
fact that giving a 1 is strategically dominated by giving a 2 isn't that
important, and the extra expressive power of giving a 1 is worthwhile.

If voters calibrate so that about half of viable candidates are eliminated
based on their median score, and if you use a voter model with
upward-skewed utilities, this class of voting systems could easily show a
VSE better than that of score voting.

I think this is a very, very promising system. Good to great VSE (it will
beat approval robustly, and could beat score under some assumptions);
easier to describe than IRV; passes summability, IIA, FBC, LNHelp,
majority, and weakened criteria related to mutual majority, consistency,
participation, LNHarm; deals well with both chicken dilemma and center
squeeze; naive vote is generally strategically optimal or close to it (the
only exception being in a center squeeze scenario, where there are two
separate strategies two factions, either of which could independently
ensure the CW wins, and where both such strategies are semi-honest and
relatively intuitively obvious.)

It still lacks some of the voter simplicity and the strategy-freeness of
SODA, but it gets there without requiring participation by the candidates.

I invite people to try to find the stickiest pathology you can for SARA.
Give honest utilities for each faction, and if relevant something about
what kind of information/strategic assumptions they're working with, and
then give their strategic ballots. I bet that even when you're deliberately
going for a pathology, you'll have a very hard time making one where the
winner isn't either the CW or among the best utility outcomes. (That is,
unless you use cheap tricks like utility monsters
<http://www.smbc-comics.com/comic/2012-04-03>.) And generally, there will
also be some relatively obvious and relatively stable strategy which
improves matters (either in terms of getting the honest CW if they exist,
or in terms of getting a higher-utility outcome).
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