[EM] The Ultimate Lottery Method!
Abd ul-Rahman Lomax
abd at lomaxdesign.com
Wed Jan 7 08:33:19 PST 2009
I wonder if it has been noticed that elections are generally
lotteries. Each voter has one vote they "own" and "pay."
The risk is that the vote is useless. The payoff is that the vote is
effective. Most votes are useless, most of the time. However, in most
systems, there are conditions where many votes pay, i.e., ties or
near-ties, where the result would change without the vote being as it
was. Sometimes the payoff is negative, in non-monotonic systems, with
poor voting strategy in some other systems.
This is what I think Dhillon and Mertens are referring to when they
say that Relative Utilitarianism votes are votes on lotteries.
We don't need, necessarily, external or additional incentives to
encourage sincere voting in a Range system, though I do think that
setting an explicit approval cutoff and using runoffs in the presence
of majority or condorcet failure will tend to encourage more accurate
voting of preferences, given adequate Range resolution.
"Runoffs" are not necessarily top two, who would be the best
candidates to go into the runoff would be a matter for the specific
conditions. A condorcet winner should always be in the runoff.
Runoffs, again, exert a force toward increased accuracy in voting.
Voters face a choice: vote narrowly, basically magnifying their
preference scale to place a large gap between their favorite and the
next-best among the frontrunners, and thus risk the need for a
runoff, or lower that gap to more accurately reflect their absolute
preference strength, or eliminate it to maximize the vote for the
pair. The incentive to avoid a runoff (or, in some cases, to cause
one), again, is one which pushes toward votes which maximize overall utility.
Turnout is a factor which has largely been ignored, as well as voter
readjustment of preferences.
Turnout in the first election might be depressed by hopelessness, by
a sense that the voter's vote will be useless. If a candidate the
voter could actually support makes it to the runoff, in spite of
this, the voter may then vote in the runoff. It happens. Runoff
turnout is different from runoff in the primary. Usually those
criticizing runoff voting consider this a problem, it is actually a feature.
Turnout reflects voter assessment of how important the choice to be
made is. That is, turnout pushes results from any system toward
utility maximization. Voters who don't care (for whatever reason), or
who don't care strongly (and in an absolute sense) don't vote, thus
leaving the election to those with stronger preference, which would
push results toward Range results, even if the method is Plurality or
another ranked system.
Turnout in runoffs is not always lower than the primary. Sometimes it
is higher. Lower turnout reflects something which should be obvious:
the better the choice of who appears in the top two, the less overall
preference strength there is between them. For many voters *it
doesn't matter* who wins! -- so they don't vote. (The same effect
operates if the two candidates (in Top Two) are both good or both
bad; in the latter case, turnout *might* still increase or be
maintained if write-in votes are allowed. That can happen. Write-in
candidates have won top-two runoff elections. At least I know of one,
Long Beach, CA mayoral election, recently. In San Francisco, it's
possible that a write-in candidate would have won if the Calif
Supreme Court hadn't ruled that a runoff election is part of the same
election as the primary, and that therefore write-ins could be
prohibited; by default, though, in California, they are permitted.
Now, did any voting systems experts notice this case when it
happened? Did any of us realize that San Francisco deprived voters of
a right that they previously had? The case took place *after* San
Francisco voters approved RCV. I think it was the last runoff
election San Francisco scheduled.)
Quite simply, the focus on single-ballot methods, i.e., fully
deterministic ones (ties excepted), caused us to miss what is
probably the most advanced voting system used in the U.S.: top two
runoff. The lack of theoretical work meant that, where IRV promoters
have moved to replace TTR with IRV, those who smelled a rat, so to
speak, had no theoretical ammunition. The arguments had not been
developed, and even when IRV proponents -- and dupes -- advanced
clearly false arguments, it wasn't even noticed.
Top Two Runoff has problems, to be sure. However, there are much
better solutions to those problems than IRV, which reproduces the
worst problem of TTR (center squeeze) -- though with reduced
frequency -- and which, in nonpartisan elections, in practice,
reproduces, more exactly that I would ever have expected, Plurality results.
We may not need a very complex system. Majority approval of the
result is a crucial aspect, one which has been missed by voting
systems experts, as if it were not important. Hence we see arguments
over which plurality winner, in a close election, should win. As has
been noted, a Condorcet winner can be a winner without majority
approval. This is different from the Majority criterion, of course.
Any majority criterion winner has majority approval, but the reverse
is not necessarily true.
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