[EM] So I got an email...

[Forest Simmons]

This is a good example for the method that successively removes pairs of
the two most disparate ballots until only one ballot remains.

The distance between ballots is the Kendall-tau (or swap cost) distance.

In this case diametrically opposites ACB and BCA are maximally far apart
... three swaps to get from one to the other. . so these polar opposite
ballots are removed two at a time until only the CBA and CAB ballots are
left.  These ballots are also removed in pairs until only one pair is left,
which means that the two finish orders CAB and CBA are tied for winning
finish order.



El dom., 10 de abr. de 2022 2:35 a. m., Kristofer Munsterhjelm <
km_elmet at t-online.de> escribió:

> On 10.04.2022 03:49, robert bristow-johnson wrote:
> > ... from Rob Richie.  I am trying to be nice (because I'm in the
> > last throes of my struggle to keep Vermont from repeating a mistake) and
> I
> > saw a small numerical error in the FV page at
> > https://www.fairvote.org/research_rcvwinners  regarding non-monotonicity
> > (and Burlington 2009).  So I wrote him (the first time since 2017) and
> > he wrote back.  That's a lot better than I can say for Aaron Hamlin.
>
> > Anyway, in our friendly back-and-forth, Rob brought up a contrived
> > example of an election where they purport that Hare works better than
> > Condorcet.  In this rhetorical example there is a dead-tie symmetry.
> > And Rob suggested that it gets resolved with "RCV - Jump ball" or "jump
> > ballot".  What, exactly, is "jump ballot"?  Is it drawing a ballot out
> > of the entire pile at random?  Like sortition?
>
> > FYI This is the context:
> >
> > ___________________________
> >
> >
> > A and B, polarizing candidates
> > C is Condorcet candidate in third
> >
> > 1st choices
> > A - 40%
> > B - 40%
> > C - 20%
> >
> > Preferences (honest)
> > ACB - 40%
> > BCA - 40%
> > CAB - 10%
> > CBA - 10%
> >
> > RCV - Jump ball
> > Condorcet - C wins 60%-40% over both A and B
>
> I don't know what "jump ballot" is, either. A plain IRV calculation from
> Rob LeGrand's calculator
>
> https://web.archive.org/web/20200813191652/http://www.cs.angelo.edu/~rlegrand/rbvote/calc.html
> says:
>
> 40: A>C>B
> 40: B>C>A
> 10: C>A>B
> 10: C>B>A
>
> C is eliminated, then A and B are tied and some tiebreaker must be
> employed.
>
> IMHO, Rob should have broken the symmetry, say
>
> 41: A>C>B
> 40: B>C>A
> 10: C>A>B
>  9: C>B>A
>
> to muddy the waters as little as possible. Perhaps "jump ballot" is his
> word for "needs a tiebreaker"?
>
> In any case, this looks a bit like center squeeze (A and B are the wing
> candidates and C is the center).
>
> > BUT... polls show this to be the case, and backers of A and B both
> > know the only way they can win is to keep C out of it. So their backers
> > bury C
> >
> > Preferences (strategic, both major campaigns)
> > ABC - 40%
> > BAC - 40%
> > CAB - 10%
> > CBA - 10%
>
> I.e.
>
> 40: A>B>C (honest A>C>B)
> 40: B>A>C (honest B>C>A)
> 10: C>A>B (no change)
> 10: C>B>A (no change)
>

In this case the most disparate pairs are ...
(ABC,CBA) and (BAC, CAB)

After removing ten of each of the pairs, we are left with

30 ABC
30 BAC

These two finish orders are tied.

Do the A or B supporters prefer a coin flip between these orders over a
coin flip between the sincere tied finish orders CAB and CBA?

Look at the geometry of the rank orders:

abc, ACB , CAB, CBA,  BCA, bac

The insincere orders are in lower case.

The question is how likely is it that the A supporters, for example, would
prefer a coin toss between the two outer most orders over a coin toss
between the two inner most orders?



> > C is no longer the condorcet winner, as both A and B seem to defeat C
> > by 80-20.  The winner will be decided by a jump ballot tally between
> > Aand B. Strategy worked.
> This is a DH3-ish situation. C is the Condorcet loser, so in every
> Condorcet method that passes Condorcet loser, the result is a perfect
> tie between A and B, further suggesting that what he means by "jump
> ballot" is "a tie that must be broken".
>
> My first observation is that if we assume that C is the proper winner in
> this particular example, then Condorcet dominates IRV in the game
> theoretical sense here, because Condorcet gets it wrong in the presence
> of strategy, but IRV gets it wrong even without strategy. Or as Warren
> put it:
>
>         - The pathology can occur with certain patterns of votes *and*
> plotting.
>         - IRV has problems that can occur without plotting.
>         - So, NO SALE!
>
> Anyway, since it is a DH3 situation, we need to first check what happens
> when one of the factions bury, because if that backfires, there's no
> incentive to bury in the first place.
>
> So suppose that we use BTR-IRV and the B-voters bury first...
> > Let's suppose only one side decides to do this. It probably backfires,
> but still gives them a chance depending on the tiebreaker., So you might
> get:
> >
> > Preferences (strategic, only 1 major campaign - backers of B)
> > ACB - 40%
> > BAC - 40%
> > CAB - 10%
> > CBA - 10%
>
> i.e.
>
> 40: A>C>B (no change)
> 40: B>A>C (honest B>C>A)
> 10: C>A>B (no change)
> 10: C>B>A (no change)
>
> For BTR-IRV, the first round Plurality loser is C. The runner-up has to
> be chosen at random from {A, B}. Since the example is completely
> symmetrical, there's a 50-50 chance of either. So the burial works if
> the B voters consider C worse than a 50-50 chance at either A or B.[1]
>
> More generally, with any method that elects from the Schwartz set, A
> wins, as Kevin pointed out. So then there's no incentive for the B group
> to bury because that only changes the winner from C (someone they rank
> second) to A (someone they rank third).
>
> Since the example is completely symmetrical, the same holds for the A
> faction. So neither faction has an incentive to bury in methods that
> pass Schwartz.
>
> So if there's anything to take from this (from a Condorcet proponent
> perspective), I'd say it's these two things:
>
>         1. A method that passes Schwartz eliminates the bury incentive for
> this
> particular election.
>         2. BTR-IRV does no worse than IRV for this election when there's
> strategy, and does strictly better with honesty.
>
> > About my struggle in Vermont: I have gotten the attention of several
> > legislators in Vermont.  Several RCV bills have stalled and languished
> > in committee and will die when this legislative session ends at year's
> > end.  But the Burlington RCV charter change has been revived and has
> > passed the Vermont House (but they took out the specific language of
> > exactly how the RCV election method will work, bumping that back to
> > Burlington city council).  It's going before the Vermont Senate
> > Government Operations Committee in the near future and I expect to be
> > visiting the state capitol again to lobby.
>
> Let's hope it will be Condorcet.
>
> -km
>
> [1]  Of course, if C is closer to B than A, the B faction wouldn't bury,
> but since the example is symmetrical, you could then argue that it's the
> A faction who buries, because now *they* have an incentive... as long as
> they're not too risk averse.
> ----
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> info
>
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