[Election-Methods] Participation failiure

[Michael Ossipoff]

Warren says, about participation failure:

IMPORTANCE:
The (conjectured) fact that this pathology is 100% common if
the number of candidates is made large, seems important...

I reply:

...if you ignore the small probability that it will happen for a particular 
voter.

If the universe is infinite, and therefore has infitely many planets nearly 
identical to Earth, and they're all using Condorcet, then it wouldn't 
surprise me if the probability of a participation failure every 4 years is 
very close to 1 or equal to 1.  But the probability that means something is 
the probability that it will happen for a particular voter in a particular 
election.

That danger is thoroughly outweighed by Condorcet's strategic benefits for 
the voter.

Mike Ossipoff


Warren said (I'm copying the posting, but my only reply to it is what I 
wrote above):

PARTICIPATION FAILURE PROBABILITY
---------------------------------

Call an election situation a "participation failure scenario"
if there exists a vote Q, such that adding some number T>0 of
honest Q-voters, will cause the election result to worsen in their view.

(This is a "no-show paradox" - these extra voters are better off staying 
home.)

The "random election model" is V voters, V-->infinity,
all independently casting random votes (all votes equally likely).

IRV-3: I did some analysis and concluded the probability that a random
3-candidate IRV election is a participation failure scenario, is 16.2%.

COND-4:  I can prove the probability P than a random
4-candidate Condorcet election, is a participation failure scenario,
is bounded below by a positive constant independent of which-flavor
of Condorcet you use.

For two particular Condorcet methods, I estimated P by monte-carlo
and it is safe to say  0.5% < P < 5%  and my best guess is 2.5%.
(My program does not compute P exactly, it only finds high-confidence
bounds on it.  If I were less lazy I could tighten the bounds...)

COOL OPEN QUESTIONS
-------------------

I suspect:

COND-INFINITY:
Random C-candidate Condorcet elections are
participation failure scenarios with probability-->1
when C is made large.

IRV-INFINITY:
Random C-candidate IRV elections are
participation failure scenarios with probability-->1
when C is made large.

I have not proven either.  I have got something close to a
proof for three particular Condorcet methods
(Copeland, Simpson-Kramer MinMax, and basic Condorcet)
although even in these cases my proof could be attacked as not
really being a proof (argument is pretty convincing, but not
fully a proof).

For IRV, P is easily seen to be a non-decreasing function of C
so it must approach a limit.

IMPORTANCE:
The (conjectured) fact that this pathology is 100% common if
the number of candidates is made large, seems important...

Warren D. Smith
http://rangevoting.org