[EM] Does IRV elect "majority winners?"

[Kristofer Munsterhjelm]

Paul Kislanko wrote:
> I don't believe RRs or practical implementations thereof define percentages
> this way.
> 
> For instance, the US Senate rules call for 60 votes, not 60% of the Senators
> who vote, in their rules. Likewise by leaving the state, for a time Texas
> Democrats delayed the (ridiculous) re-districting plan the Republicans
> eventually got passed anyway by just reducing the numerator for a fixed
> denominator.
> 
> Legislatures who follow RRoO pretty much define majority by "majority of
> eligible voters." If we want to depend upon majority-criteria we need to
> pick whether we mean majority of voters or majority of eligible voters. If
> we chose the latter definition then NO method can make such a claim, unless
> it has a specific method for dealing with non-voters.
> 
> If we chose the "majority of voters" approach, then Bucklin is an efficient
> way to find all majorities that support any alternative. IRV is problematic,
> because the method changes the definition of "voters" in each round. I'm not
> sure IRV is unconstitutional, but it is repugnant.

In another respect, Condorcet is an efficient way to find majorities 
that support an alternative. If we (for the sake of simplicity) assume 
voters are sincere and runoffs have similar turnout as primaries, then 
if X pairwise beats Y, X would beat Y in a runoff. If X's a sincere CW, 
it win a runoff, no matter who it ran against.

There are confounding factors: voters may employ strategy, and Abd's 
point that only the voters that care show up for the runoff may be true. 
However, these factors will exist for Bucklin (and IRV and any other 
method) as well.

By considering the runoff process in this manner, we find that runoffs 
aren't magic - they only ensure that a sincere Condorcet loser won't be 
elected, and if there's a sincere CW and the CW is in the runoff, that 
said CW will win. If you had a pessimal primary method that picked the 
two last place candidates in a Condorcet method after the Condorcet 
loser had been removed, and the ballots were sincere, the runoff would 
still pick a bad candidate (unless number of candidates = 3). If a 
runoff provides "majority support", then that bad candidate would be 
"supported by a majority".

Still, there's one important thing to remember when dealing with 
(two-candidate) runoffs: the second round will be sincere, since there 
are just two candidates and the simple "whoever gets the most votes 
wins" is strategyproof for two candidates. This means that the strategy 
employed will be focused on the first round (the "primary") to pass the 
strategists' preferred candidates for the second round. Also, even if 
they succeed in making the system pass one candidate to the next round, 
they'll fail if the other candidate is preferred to him (sincerely).