[EM] Does IRV elect "majority winners?"

[Kristofer Munsterhjelm]

Abd ul-Rahman Lomax wrote:
> At 05:15 AM 1/7/2009, Kristofer Munsterhjelm wrote:
>> Dave Ketchum wrote:
[snip]
>> On the other hand, the mayor election data that was given on this list 
>> earlier seems to show that people don't bullet-vote as much as one 
>> would expect (even though one should be careful in deriving 
>> conclusions from sample sizes of one).
> 
> It showed this for *that* election. Burlington is a very unusual town, 
> and there can be a lot of enthusiasm for preferential methods at first 
> (there was a lot of enthusiasm for Bucklin at first.) We should look at 
> the San Francisco data for more evidence. In Australia, experience with 
> Optional Preferential Voting shows that bullet voting tends to increase 
> with time, after full ranking becomes optional, as voters realize that 
> full ranking is mostly a waste of time. Most voters can simply bullet 
> vote for a frontrunner, in most elections, and if they do rank lower, it 
> is never even counted. Only those who support minor party candidates 
> need add additional ranks.

This may mean that people start off "innocent" - that is, they don't 
know about strategy or truncation, etc. Then, as they grow more familiar 
with the method, they know what works and what doesn't. I have no proof 
of this, though; we'd need ballot images for the very first election (or 
one of the first), and then of later elections, to compare the two.

If I'm right, that may mean that claims in favor of Range (e.g the 
"nursery effect") would only be temporary as more and more switch to 
voting Approval-style.

>>> Bucklin deserves more thought as a competitor to Condorcet.
>>
>> Bucklin doesn't do that well, Yee-wise. It's simple, however; I'll 
>> grant that. As far as criteria go, it fails independence of clones, is 
>> not reversal symmetric, and can elect a Condorcet loser (according to 
>> WP).
> 
> Don't trust Wikipedia for *anything*. It is not to be used as a source. 

Alright. I'll try to find other sources, and also mention a criterion of 
Benham's: IIR - if you add a candidate that loses (pairwise) to all 
others and the only ballots you add are those that plump for it 
(bullet-vote), then that shouldn't alter the election.

In Bucklin, it does. By adding an insignificant candidate, the majority 
threshold is increased so that some other may get the majority.

Regarding clone-proofing, Rangevoting.org says this:

"Similarly, ER-Bucklin is clone-immune with clones equality-ranked, but 
not with preferences among the clones, since cloning the winner can 
cause all winner-clones to be delayed in acquiring the necessary 
vote-majority, allowing somebody else to win sooner."

(http://rangevoting.org/FBCsurvey.html)

Rob LeGrand showed an instance of Bucklin not being cloneproof:

20:A>B>C
17:B>C>A
13:C>A>B

so B wins by majority in the second round, but then clone A

20:D>A>B>C
17:B>C>A>D
13:C>A>D>B

and A wins by majority in the second round, having pushed the 
B-preferences down.

(http://www.mail-archive.com/election-methods-electorama.com@electorama.com
/msg02705.html )

http://www.condorcet.org/emr/methods.shtml also says Bucklin fails 
Condorcet Loser, Consistency, LIIA (obviously), Reversal Symmetry, "SPC" 
(really LNHarm; again, obviously), and Smith. That page's maintained by 
Blake Cretney.

Schulze shows Bucklin fail reversal symmetry here: 
http://www.mail-archive.com/election-methods-electorama.com@electorama.com
/msg00893.html

19  A > C > B
20  B > C > A
  1  C > A > B
  1  C > B > A
  1  B > A > C
  1  A > B > C

Running it "forwards", C wins in the second stage. Running it backwards, 
C also wins in the second stage.

Consistency isn't that important. The method obviously fails LIIA if it 
fails Smith, which it does (and must since it fails Condorcet Loser). We 
know Bucklin fails LNHarm because it passes LNHelp and mutual majority, 
yet is monotonic.

> I don't trust much of the simulation work that's been done, because of 
> lack of simulation of truncation, for example. Truncation is *normal.* 
> With Bucklin elections, maybe two-thirds of the voters don't add 
> additional preferences.

So let's look at the data.

> Bucklin, further, as it was implemented, didn't allow multiple voting in 
> the first and second rounds. I'd toss that restriction, I see no need to 
> *force* voters to rank candidates; if they have sufficient preference 
> strength between them, they will rank them, if not, they may not. This 
> would make Bucklin even more like Approval.
> 
> And simulating approval realistically is far more difficult than 
> simulating ranked methods. Most simulations of approval have made wild 
> assumptions that voters will, for example, approve any candidate better 
> than the mean utility. It's preposterous, voters won't vote that way.

If you want something explicitly Approval-esque, why not use MDDA? MDDA 
is: those candidates people rank count as "approved". Those they omit 
don't. First eliminate all candidates that are beaten by some other 
candidate by a majority (unless that eliminates all of them). Then count 
the approved candidates that remain.

As a voter, you'll have the problem of setting the Approval cutoff, but 
that's pretty much a given for Approval-esque methods.

>> Range reduces to Approval if enough people use strategy. I think that 
>> any version of cardinal ratings should either be DSV or have some sort 
>> of Condorcet analysis (like CWP does, or perhaps not that far). Those 
>> are my opinions, though, and others (like Abd) may disagree.
> 
> I think that Condorcet analysis should be done with Range ballots, but 
> that a Condorcet winner, when different from the Range winner (unusual) 
> should not automatically win, but there should be a runoff. In theory -- 
> my theory -- the Range winner is better, but there are conditions where 
> this isn't accurate, and a runoff tests those. Generally, whenever the 
> majority gives up its first preference in favor of a more strongly 
> preferred minority choice, the majority should consent to this.
> 
> Condorcet analysis, note, would encourage a shift away from pure 
> Approval Voting. So, too, would running a Range election in rounds, 
> i.e., Bucklin.
> 
> Oklahoma tried to implement a Range Bucklin method, but erred in trying 
> to require additional ranking.
> 
> Essentially, the approval cutoff, for elections purposes, would be 
> lowered through the ratings until a majority appears, that would be the 
> Range winner. Condorcet analysis would detect if there was a Condorcet 
> problem, and if there is an absolute approval cutoff, majority failure 
> would also be a runoff trigger.
> 
> Basically, a method should be able to detect that the electorate hasn't 
> yet made up its collective mind.

I would accept that, but for another reason: that I think the Condorcet 
winner would win more often than the Range winner. If it, to you, lets 
the Range winner win, and to me, lets the Condorcet winner win 
(depending on which of us are right), then we could both accept it 
(unless it burdens the voters too much).

It's not my favorite, but I would accept it.

You say VNM is natural; to me it seems that having to optimize like that 
would definitely burden the voters. They have to figure out "my response 
to their responses to my response to their responses"... which sounds 
more like a game of chess than an election method. That the burden means 
that only those who are dedicated (have strong preference strength) 
bother to optimize might be true, but note that this will favor central 
organizations that can direct its subordinates to calculate the strategy 
(i.e. party vote management).

But I digress.

> It's really silly. A fax machine can adequately scan any 
> reasonably-designed ballot. Normal scanners can handle it. Burlington, 
> in fact, used a cobbed-together solution with scanners and open source 
> software.

That should work. Open source would be an advantage because you can 
check the code for errors. Better yet would be to have machines that are 
very modular with each part not Turing complete (so no trickery can be 
done through miscounts), but well, some is better than none.

> I've promoted "public ballot imaging," which simply means that the raw 
> images that scanners or faxes or whatever produce, become public, and 
> further implies that election observers can independently image ballots. 
> Digital cameras would do the job just fine. A single camera, current 
> technology, can hold all the ballots from a precinct without difficulty.

That seems very susceptible to vote-selling. Say I sell votes. I say 
"vote my way and draw a smiley face in the upper right corner, then I'll 
reward you" (or some other place, differing for each person). When the 
raw images are available, I simply check wheter some of them voted my 
way and have smileys in the right places. Then I can pay those who sold 
their votes.

It's simple to turn this into coercion, e.g "vote my way or someone will 
come to your house with a baseball bat". Vote-selling is less overtly 
criminal, though.

>> The ideal solution as far as granularity is concerned would be to have 
>> a machine that does OCR, and where voters just write a number in a box 
>> next to the candidate (1 for first place, 20 for twentieth). That 
>> would be quite a bit more expensive, though, and would also need some 
>> sort of fallback... or just manual counting.
> 
> Use standard mark-sense technology. However, with Bucklin, I see no need 
> for more than three ranks. It's highly questionable that the lower 
> rankings as with the Burlington election means much at all. We may find 
> a technical Condorcet winner, but it's actually meaningless in terms of 
> how the voters view that candidate, if it's based on lower rankings.

If you view Bucklin as an extension of Approval, that would be true, but 
some voters may not.