[EM] DSV: A way to restore monotonicity?

[Kristofer Munsterhjelm]

I may have found a way to either restore monotonicity or reduce 
nonmonotonicity to a method. This is quite good if true, so I'd want 
others to check before I run around saying I've done something nobody 
has before :-)

"Contingent vote with donation": Suppose we have an A>B>C>A cycle and 
that A and C advance to the final. Then A might have preferred to have 
fewer first preferences - for some of his voters to have voted BAC 
instead of ABC - so that B would've advanced to the final instead, and A 
would beat B pairwise and win.

The method I just does this: when it checks a finalist pair A and C, it 
sees if there's a way of A to transfer some of his first preferences to 
another candidate B so that:
	- A remains in the top two
	- C is pushed off the top two
	- A beats B pairwise more than A beats C.

If so, then A's score is given as the maximum of A>B and A>C, not just 
A>C as it would otherwise be. (My scoring scheme is, in the absence of 
any first preference donations, that the top two candidates X and Y get 
scores X>Y and Y>X respectively, and everybody else gets zero. Ties are 
handled by A getting max A>B over any B that could be in a finalist 
pairing with A. This is slightly more strategy resistant than just 
taking the mean score.)

And that seems to rid the method of its nonmonotonicity! In return the 
strategy susceptibility increases quite a lot, but (if true) it's the 
most resistant summable method I know of yet - just barely beating fpA - 
max fpC, even on 3 candidates.

Note that I don't have an actual monotonicity detector in quadelect yet. 
The only thing I'm going by is that pushover strategy would be detected 
as "Other" strategy, because it's neither burial nor compromising nor 
two-sided. Thus "Other" going to zero or near-zero is a good indication. 
It would still have to be verified, though.

And furthermore, I think there's room for more optimization. I don't yet 
check if A can be on the losing end of a donation, e.g. {A, B} is a 
finalist pair but C could displace B. So in this case, A would get A>B 
but should (arguably?) get zero instead, which might help strategy 
resistance.

Still!

I also did some experimentation with Quick Runoff. It's not very 
strategy resistant, so while I proposed a similar idea to Kevin, I don't 
think I'm going to implement it yet.

Something else that's strange is that sometimes X is less strategy 
resistant than Smith,X even though X passes the InfMC. Some of the time 
it's due to ties, but I'm not sure if that's all there is - yet another 
reason others should check things out or try variants.

Stats:

The methods are:
IFFP-like, fpA-sum fpC, fpA-max fpC, IFPP, IRV: as in the previous post
Contingent: Contingent vote
Donation: Contingent vote with donation
QRunoff: Quick Runoff with the same A>B>C>D.. tiebreaker (not strictly 
speaking anonymous)
IRV: IRV with the same tiebreaker

Impartial culture, 97 voters, 3 candidates, 75000 elections, 512 Other 
attempts per:

(Here every fpA-fpC method is the same so I'm just going to list one of 
them. IRV and Contingent differ due to their different tiebreakers.)

                    ties    burial  compromise  two-sided   other  total
Smith,fpA-max fpC: 0       0.0665  0.0878      0.0153      0      0.1696
Smith,Donation:    0.0043  0.0616  0.0818      0.0240      0      0.1675
Donation:          0.0117  0       0.1214      0.0407      0      0.1621
Smith,Contingent:  0.0023  0.0346  0.0856      0           0.0175 0.1377
Contingent:        0.0054  0       0.1209      0           0.0213 0.1422
Smith,QRunoff:     0       0.2027  0.0876      1e-05       0.4541 0.7444
Smith,IRV:         0       0.0343  0.0855      3e-05       0.0236 0.1434
Smith,IFPP:        0       0.0687  0.0856      0.0158      0      0.1702

Impartial culture, 97 voters, 4 candidates, 75000 elections, 512 tries:

                    ties    burial  compromise  two-sided   other  total
Smith,IFPP-like:   0.0225  0.2576  0.1296      0.5071      0      0.8943
IFPP-like:         0.0996  0       0.8838      0           0      0.8838
Smith,fpA-sum fpC: 0.0097  0.4215  0.0963      0.3758      0      0.8936
Smith,fpA-max fpC: 0.0113  0.1534  0.1474      0.3920      0      0.6923
Smith,Donation:    0.0056  0.1074  0.1647      0.3872      1e-05  0.6593
Smith//Donation:   0.0073  0.1263  0.1449      0.3870      3e-04  0.6586
Donation:          0.0147  0.0452  0.6091      0           4e-05  0.6544
Smith,Contingent:  0.0036  0.0815  0.1700      0.0004      0.2045 0.4565
Contingent:        0.0096  0       0.2614      0           0.2385 0.5000
Smith,QRunoff:     0       0.2677  0.1561      0.0007      0.5105 0.9349
Smith,IRV:         0       0.0555  0.1741      5e-05       0.0497 0.2794
Smith,IFPP:        0       0.0973  0.1653      0.0156      0.0496 0.3277

-km