[EM] Election methods in student government...

[Kevin Venzke]

Tim,

--- Tim Hull <thully at umich.edu> a écrit :
> DSC uses a somewhat interesting method - it effectively goes and excludes
> the groups of candidates that the most people prefer a "solid coalition"
> to
> until it finds a winner.  However, what I am wondering is - what are the
> primary flaws of these two methods (especially as compared with IRV, of
> which I know quite a bit about the flaws)?

DSC will render your vote useless if you list a nobody as your favorite
candidate. (Just like under FPP.) IRV will eliminate that candidate and
allow your vote to be useful elsewhere.

(Also, I hate programming DSC, and I'm not positive what the cloneproof
thing to do is when multiple sets are tied.)

So even though DSC is monotonic and gives real incentive to fill out the
ballot completely (it fails LNHelp), I don't like it better than IRV.

For majority defeat disqualification + first preferences (let's call it
"MDD,FPP" using Woodall's comma notation to show that we don't eliminate
candidates prior to finding the FPP scores), in a single round, the
biggest problem is iffy winners. That is, it will toss out candidates
who lose a majority decision. But rather than give the win to someone
who *won* a majority decision, it gives it to whoever had the next
greatest number of first preferences. This same example:

49 A
24 B
27 C>B

A is ruled out due to a majority loss to B. But it can be shown that
B must not be elected, if we're satisfying LNHarm. MDD,FPP elects C,
which is a failure of Woodall's "Plurality criterion."

I'd note that MDD,FPP is much better than MMPO here, though.

MDD,FPP is also vulnerable to burial strategy:

40 A>C  (but actual sentiment is A>B)
35 B>A  (sincere; they feel free to vote A due to LNHarm)
25 C>B  (sincere)

The 40 voters can take advantage of the assumption that the 35 voters
will vote for A. B wins when the 40 voters just vote "A", but when they
vote "A>C," this makes A win.

To stop this, the 35 voters need the 40 voters to be uncertain about
whether they will truly vote B>A. (Also, if the 25 voters don't strictly
rank C above B, they can also stop this.) Because if the 35 voters vote
just "B", then the 40 voters will accidentally elect C if they vote
insincerely.

My main criticism of MDD,FPP-plus-runoff is that if you view both rounds 
of the method as a unit, it doesn't satisfy LNHarm. Your lower 
preferences can affect who your candidate has to compete with in the
second round.

(Also, having two rounds may be undesirable. And also, I'd prefer a
version where you can list multiple first preferences, but that is not
sensible if you're going to have a runoff.)

>  I know all later-no-harm
> satisfying methods have more flaws than methods that don't satisfy it,

That's a matter of opinion and your priorities. I would say the common
side-effect of LNHarm is that voters may need to rank compromise choices
higher than if they voted sincerely.

> Frankly, I'm surprised more methods have not been
> developed that satisfy this criterion, as it would seem like an important
> one if you want people to vote honestly.

It is important, but there are just not that many ways to satisfy it.
It inherently hampers the way that compromise choices can be used.

Another criterion is the favorite betrayal criterion, which roughly says
that you can't ever help your favorite candidates by not voting for one
of them. Satisfying this criterion, you can at least be assured that you
will actually get people's real first preferences. (They just might be
tied with some other compromise choices.)

This is satisfied by e.g. Approval, MMPO, the MTR method (which is
just three-slot MDD,FPP with equal ranking allowed), my ICA method 
(which is almost Condorcet-efficient), and one version of Bucklin.

> Also, does anyone have a clue as to how one would go about developing a
> multi-winner PR version of these methods?  THAT sounds like an
> interesting
> prospect to me, as STV is currently the only method out there for pure
> multi-winner PR that satisfies LNH (not counting party lists, asset
> voting,
> and other nontraditional methods)

I'm not too sure. For DSC and MMPO, I have no idea how you would determine
fairly that a ballot has contributed to a given candidate's election.

I suppose it matters what it is you find lacking about STV. Whatever it
is I suspect there is no good solution for it, though.

Kevin Venzke


	

	
		
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