James Gilmour wrote:
Kevin Venzke > Sent: Tuesday, December 16, 2008 1:49 PM
The reason I believe LNHarm is more valuable than
monotonicity is that when a method fails LNHarm, the voter is
more likely to realize in what insincere way to vote
differently, in order to compensate. When a method fails
monotonicity, a voter will rarely know to do anything
differently because of it.
LNH is important to ordinary electors, as I have explained in a
recent post, at least where the voting system is susceptible to LNH
effects. If the vote counting method is not LNH-compliant, electors
are likely to vote strategically in an attempt to avoid or
mitigate the effects of LNH-failure or to try to gain some real or
imagined advantage from its effects.
Monotonicity, or more specifically, the lack of monotonicity, is of
no importance whatsoever in public elections because neither
candidates nor voters can exploit it. It would be "nice" if the vote
counting system were monotonic, but we cannot have
monotonicity AND some of the other criteria we consider desirable.
For example, monotonicity and later-no-harm are incompatible in
IRV and STV-PR. Of the two, LNH is important - non-monotonicity is
irrelevant.
We can't have both LNHs, mutual majority, and monotonicity (by Woodall).
FPTP has LNH* (simply because later choices are ignored) and
monotonicity. IRV has LNH* and mutual majority, but not monotonicity.
I'd say that IRV's monotonicity problem is indeed a problem, because
it's so pervasive. Just look at Yee diagrams. On the other hand, I'm not
unbiased, and so I may be saying that because it's "unaesthetic".
In any case, it may be possible to have one of the LNHs and be monotonic
and have mutual majority. I'm not sure, but perhaps (doesn't one of DAC
or DSC do this?). If so, it would be possible to see (at least) whether
people strategize in the direction of early truncation by looking at
methods that fail LNHarm but pass LNHelp; that is, Bucklin. Was bullet
voting pervasive under Bucklin?
Unfortunately, no method that passes only LNHarm has been used, so we
can't do the same there (to see if there was pervasive random filling in
that case).
We can stil get some idea of how easily voters would strategize by
looking at Bucklin, though; or for that matter, at ranked voting methods
that fail both LNHs. Schulze's used in some technical associations
(Debian, Wikimedia), and, although I don't have raw voting data, they
seem to be mostly honest. The Wikimedia election had no Condorcet cycles
down to the sixth place, for instance.
James Gilmour
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