[EM] So I got an email...

[Kristofer Munsterhjelm]

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)

> 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.