[EM] The easiest method to 'tolerate'

[Kristofer Munsterhjelm]

On 06/29/2016 01:03 AM, Kevin Venzke wrote:
> Hi Steve,
> 
> Majority Judgment is a variety of "median rating" methods which I see as
> pretty similar. Woodall made one himself called Quota-Limited
> Trickle-Down and in fact if you google "woodall qltd" you can find a
> .pdf with a chart of some of the properties. The most noteworthy here
> are the failures of Later-no-harm and Mono-add-top. (Both are failures
> that IRV does not share.) For Later-no-harm: Suppose that candidate A is
> elected. It's possible that there is a bloc of voters who rated B above
> A, but A above zero, and that if these voters had lowered their A rating
> to zero, then candidate B would win instead, which is an outcome this
> bloc of voters would have preferred. They could criticize that the
> method should be smart enough to not use their A ratings to elect A when
> it would have been possible for them to elect B. If not a fairness
> issue, it's at least an issue of the method requiring voters to keep
> certain strategy in mind.

I'll also note that MJ fails

- Participation: Failure means that a voter might make the outcome worse
from his point of view by going to the polls. (Participation is
notoriously hard to pass)

- All-equal ballots irrelevance: you can have a voter show up and give
every candidate the same rank, yet that changes the outcome. You'd
expect that to pull every candidate equally in the direction of the
grade that voter gave to every candidate, but that's not true.

See also, from a Range perspective: http://rangevoting.org/MedianVrange.html

> The Mono-add-top issue works like this: Suppose that C is elected. It's
> possible under median ratings methods that when some ballots rating a
> different candidate "D" first (i.e. D is the first preference) are
> removed from consideration, then a candidate D becomes the new winner.
> In other words, when C wins, the D-first voters can criticize that they
> were penalized for showing up to vote.
> 
> I should note that while IRV does not have these issues, probably *most*
> of our proposed methods do, so they aren't necessarily deal-breakers.

Incidentally, Minmax(margins) passes Condorcet and mono-add-top. It's
not one of the methods I'd call advanced, though.

> While median rating is more resistant to manipulation than Range, I
> still view the manipulation potential as bad. For example, if you
> "defensively" rate A as zero, in the Later-no-harm example above, out of
> a quite reasonable fear that you need to do this to help B win instead
> of A, this is the type of thing meant by manipulation. It is less likely
> to have an effect than in Range, but you will still have the incentive
> to do it.

There are two ways to consider strategic incentive. Suppose you have a
method whose benefit (additional utility) to a particular voter X is
something like:

http://www.wolframalpha.com/input/?i=ln%2820x%2B1%29+from+0+to+0.5

where the x axis is the size of the strategizing coalition X is part of,
when everybody not in the coalition votes honestly.

It's clear that no matter the size of X's group, X has an incentive to
strategize. A rational voter will clearly always strategize.

Now suppose the utility given to X is more like:

http://www.wolframalpha.com/input/?i=ln%2820x%2B1%29+*+%28-SquareWave[1.2*sqrt%28x%29]+%2B+1%29%2F2+from+0+to+0.5

i.e. there's a hard threshold before which strategy has absolutely no
effect, positive or negative.

A rational voter would still always strategize because there's no actual
harm to doing so, and if enough voters aligned with his candidate think
the way he does, he'll benefit. So it's a chance of getting something
better with no risk, and a rational voter would take that.

However, it seems unintuitive to me that a real voter would do so.
Instead, it seems more that voters value expressing their true
preference, and as long as the benefit to strategy is less than what
they gain by expressing their preference, honesty wins.

I have no hard proof that this is the case, and as I mentioned in
another post, there might very well be cultural differences. An
electorate accustomed to FPTP and the pervasive strategy there might be
more inclined to be strategic by default. I also seem to recall that the
parties in New York under STV almost immediately tried to game STV
through vote management, whereas according to Schulze's paper on vote
management, other countries' STV elections seem to be relatively free of
strategy.

This is another one of those questions that ultimately have to be
answered by practice. My point is that MJ has a pretty broad
not-affected threshold, but Range is more like the continuous function
above up to Approval, so if thresholds protect against strategy, MJ
would be better protected.

> Your definition for "one citizen one vote" is difficult for me because
> it seems focused on how the winner is found. For example you say
> preferences should be counted equally "as long as possible, until"
> something happens, which seems to assume that an election method
> algorithm is something that unfolds over time. Normally I view an
> election method as defined by its results, and there need not be a
> single set of steps which finds the result. I wonder what would be an
> example of a method that violates "one citizen one vote," and if there
> might be another way of describing what is problematic about it.

To repurpose a quote, "I do indeed concur. Wholeheartedly!". In my
opinion, criteria should say something about the results, not about how
the algorithm works.

It's always advantageous if the method also makes sense based on how it
works, but I'd rather have an opaque method with good compliance than
vice versa. Borda is very simple, but its extreme teaming incentive
makes it of little use in competitive elections.

That doesn't mean it's impossible to rephrase seemingly obvious
algorithm-based criteria to be more algorithm-agnostic. My post on
qualitative vote-wasting is an example of that.

If I recall correctly, Steve has stated that Nanson/Baldwin fail his
OCOV because Borda's points system takes later preferences into account.
However, it does "treat all preferences equally". If anything, IRV fails
to do so because it only looks at first preferences, yet IRV appears to
pass that OCOV criterion.