Better "Soft Quorum" Rule

For score voting when we allow "no opinion" scores...

...there is a worry, which has been pointed out by score-voting critics. It is this:

"Unknown lunatic wins" nightmare: Suppose some crazy candidate whom almost nobody has ever heard of, runs for election. He convinces a small core group of fanatics to score him maximum. Ever other voter honestly gives him "no opinion" and hence his average score is very high, and he unexpectedly wins the election.

Is this nightmare realistic? No. The reason it is not realistic is that all those people who have complained to us about this possible nightmare, will vote min-score for unknown candidates to protect themselves from the nightmare. And it is an experimental fact, which we have seen in action many times, that a large fraction of score voters give unknown-to-them candidates minimum score. It is true that many score voters also give unknown-to-them candidates "no opinion." But in our extensive poll/test experiences with real voters, the former behavior is actually substantially more common (e.g. in one study we found it was 1.7× more common).

Statistical trends like that actually become massively reliable when the number of voters becomes large. In other words: the very fear of this nightmare automatically stops it from happening.

But some people are unconvinced by all that. They still twist and turn in bed shuddering with fear of this nightmare, and want even more protection. Hence for them we offer...

The latest plan: is a score-voting system in which each candidate gets some pre-agreed number T of artificial "zero" (or other agreed fixed) scores before voting begins (e.g. 1000 zeros each). Then the highest average score wins. ("NO OPINION" votes do not affect averages, as usual.)

The optimum value of T presumably roughly equals the size of the largest set of fanatics anybody can organize to support them while at the same time staying unknown to (or at least inspiring no interest from) the rest of society. (It is very hard both to organize your fanatics and stay unknown at the same time, so I do not expect this number will be very large, percentagewise.)

The point is that, if this is done, it becomes almost impossible to win versus well-known opponents if you have a small number of supporters even if 100% of the rest of society votes "no opinion" about you. (This "soft quorum" method seems superior in various ways to older quorum rules 1, 2, which we now deprecate.)

So those who worry about that nightmare scenario now can relax.

But on the other hand, if T were made too large then that also would be bad because it would prevent excellent-quality candidates from winning just because they were insufficiently well known. For example, in the 2008 Time Magazine "person of year" contest (which was conducted via score voting) B.Obama was extremely well known but as of that date had actually done very little. He was winning Time's poll by a small margin. The second-placer was a comparatively extremely-unknown scientist, Douglas Melton, who found a breakthrough which may eventually cure diabetes. If so, he certainly is a great benefactor of humanity and deserves to win or at least place high. But if the number of artificial "zeros" were too many, then Melton would be unable to compete with Obama even if his quality was reckoned higher by everybody who knew both.

So it is bad to set the "quorum" level too high. But it also is bad to set T too low, because that would cause too many people to be too-scared about the "unknown fanatic wins" scenario. We need to employ the level that yields the optimum tradeoff.

Mathematical underpinnings of this, from puzzle 117.

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