> We could also adjust it to e.g. 49 A, 5 B, 46 C>B, with a significant
> number of the 49 voting A>B.
> My issue is not simply that C voters have strategic incentive here.
> that the incentive is to abandon candidates who aren't frontrunners;
> that it is practically risk-free; and that if the C voters don't use
> the strategy, their sincere votes confuse margins into picking the
Some comments to this example as requested:
It seems that you have corrected the previous example (49 A, 24 B, 27
C>B) so that it doesn't require all the A supporters to be strategic
to introduce the vulnerabilities.
I again assume that the intended sincere opinions follow the typical
(extreme) left-centre-right pattern, giving sincere opinions 49
A>B>C, 5 B>A=C, 46 C>B>A.
Now the strategic pattern emerges if 11 A supporters truncate (or 10
for a tie).
In this example the biggest problem is maybe the fact that the A
supporters take a big risk when they do not indicate their support to
their compromise candidate B. If their strategic calculations are not
exactly right, and there is a one vote shift in preference away from
the A faction and towards the C faction, then C will win. Note that
this risk hits them sooner (with smaller number of strategic voters)
than the benefits.
Note also that if there is a two vote shift towards the A faction
strategic voting is not needed since A faction has majority anyway.
Note also that if the A party recommends strategic voting to take the
victory away from B the B supporters might turn against A and give
their (secondary) support to C, which would again easily make C the
It may not be sensible to the A voters to risk and possibly make C
the winner by ignoring their compromise candidate. The A party might
as well try to make sure that all their supporters will vote A>B to
eliminate the risk of C winning (also B supporters might like that
and give them some additional support). Maybe you'll find another
better set of numbers. Sorry for commenting the problems one by one.
I don't have a complete theory and analysis available to present.