[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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