[EM] Does IRV elect "majority winners?"

[Abd ul-Rahman Lomax]

At 07:48 AM 1/3/2009, Kristofer Munsterhjelm wrote:

>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.

This is a common assumption, and it only holds under three 
(unrealistic) assumptions:

(1) The same voters vote in the runoff.
(2) They fully ranked in the primary.
(3) They didn't change their minds.

Preference strength affects all three of this, in a particular 
direction. Usually, yes, the Condorcet winner will win; however, I 
could also say that the Range winner will usually win. Usually, they 
are the same candidate!

So what happens when they differ? That depends on how strategic 
voting has affected the votes. Generally, though, if the Range votes, 
overall, represent realistic averaging of the voter positions, the 
Range winner will prevail in the runoff against the first-round 
Condorcet winner.

Of course, that first-round winner is no longer the Condorcet winner. 
The runoff is a separate election.

The system is Condorcet compliant, overall, because a true -- stable 
-- Condorcet winner will prevail. However, that doesn't at all mean 
that a Condorcet winner from the primary ballot (let's assume it's a 
Range ballot, so both Range and pairwise analysis may be done) will 
necessarily win.

A single runoff isn't magic, though, but it's like the old saying, 
two heads are better than one. The difference between two people 
working on a problem and just one can be drastic. Two rounds starts 
to approach, makes a large step toward, deliberative process, which 
is *intelligent*. It is not merely aggregation any more.

It starts to approach what a sound and accurately representative 
parliamentary system would do, except that we probably get better 
results if we simply create that system and allow it to select single 
winners, i.e., officers.

>  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".

I don't agree that runoffs, in themselves, necessarily provide 
"majority support," except technically. In substance, no, because of 
the restrictions. If there is no restriction, such as write-in votes 
being allowed, it's a different story. *But nobody seems to have 
noticed that we do have write-ins allowed in some runoffs, and that 
right is being chipped away by those in power.*

>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).

That's right. Two-round systems, arguably, make the best choice among 
the top two. In nonpartisan elections, turns out, about one out of 
three times, IRV gets it wrong, i.e., decides differently than the 
electorate would decide directly.