[EM] Zero-Info Probabilistic LNHe

[Michael Ossipoff]

Supporting definitions:

A zero-information (0-info) election is an election about which all
that is known is the candidates and the voting system. There's no
information about the voters, their preferences, or any predictive
information about details of the voting.

To vote a candidate at bottom is to not vote that candidate over
anyone. To vote a candidate above bottom is to vote that candidate
over someone.
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Zero-Info Probabilistic LNHe (ZLNHe):

In a 0-info election, voting above bottom one or more of some certain
set of candidates shouldn't decrease the probability that the winner
will come from that set, as compared to voting them all at bottom.

[end of ZLNHe definition]

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ZLNHe could be called a "weakening" of LNHe. But calling it "weak
LNHe" would be misleading and unfair, because it is only very slightly
weaker than LNHe.

It's easier to refer to a 0-info election than to try to name
different kinds of voting-predictive information. But the information
that actually must be absent in that criterion's scenario is
information that is usually or always absent even in non-0-info
elections. Therefore, ZLNHe is nearly the same thing as LNHe, and the
word "weakening" hardly even applies.

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Strong ZLNHe:

Same as ZLNHe, except that voting one or more members of that set over
bottom must increase the probability that the winner will come from
that set.

[end of Strong ZLNHe definition]

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Any improvement by Strong ZLNHe over ZLNHe seems much less valuable
than ZLNHe compliance itself. Not having strategic need to rank
unacceptable candidates and try to guess in what order to rank them,
is clearly a good thing.

The stronger version just seemed worth mentioning, because it's the
same thing but more-so, and more difficult to meet.

I don't have proofs of my statements about compliance and
noncompliance with these criteria, but, at first glance, it appears
that convincing arguments could be made.

Though Symmetrical ICT doesn't meet LNHe, it seems to me that it meets
ZLNHe and Strong ZLNHe.

There are convincing reasons to say that many, most, or all popular
versions of traditional unimproved Condorcet fail ZLNHe.

We've all heard the expression "Random-fill incentive", in connection
with traditional unimproved Condorcet.

(It seems clearer to set method and criterion definitions off with
horizontal lines)

Mike Ossipoff