[EM] Fwd: Duncan Proposal Draft

[Kristofer Munsterhjelm]

On 10/13/23 19:11, Forest Simmons wrote:
> Dear EM List Friends,
> 
> We need your feedback on this draft of a proposal before we submit a 
> version of it to the voting reform community at large.

This is not feedback on the draft as such, but the results of my 
strategy vulnerability tests with CTE-Borda (which I'm guessing this is).

My implementation uses bubble sort, which I understand is the same as 
sink sort (see e.g. https://xlinux.nist.gov/dads/HTML/sinkSort.html). I 
asked you if it's different, but I didn't got a response. If what you 
mean by "sink sort" differs from bubble sort, my results may be off.

In any case, the method seems to have somewhat strange behavior under 
impartial culture. With only a few voters (i.e. the election being far 
from tied), there's still burial incentive. This burial incentive 
disappears with increasing numbers of voters, but at a great cost of 
general coalition strategy (which I imagine to be, but can't verify to 
be, mostly pushover). The sum of burial and other strats push it to a 
relatively high total susceptibility, although not quite as high as the 
defeat-droppers.

Here are the stats:

Impartial culture, three candidates, 13 voters, 25k elections, 32k tests 
per election:

CTE-Borda:

Burial, no compromise:  5381    0.21524
Compromise, no burial:  2050    0.082
Burial and compromise:  0       0
Two-sided:              5085    0.2034
Other coalition strats: 4120    0.1648
==========================================
Manipulable elections:  16636   0.66544

For comparison, Schulze:

Burial, no compromise:  9988    0.426582
Compromise, no burial:  210     0.00896899
Burial and compromise:  282     0.0120441
Two-sided:              2206    0.0942171
Other coalition strats: 0       0
==========================================
Manipulable elections:  12686   0.541813

Impartial culture, five candidates, 13 voters, 25k elections, 32k tests 
per election:

CTE-Borda:

Burial, no compromise:  8654    0.34616
Compromise, no burial:  3864    0.15456
Burial and compromise:  2054    0.08216
Two-sided:              6673    0.26692
Other coalition strats: 2032    0.08128
==========================================
Manipulable elections:  23277   0.93108

Schulze again:

Burial, no compromise:  11196   0.548985
Compromise, no burial:  495     0.0242718
Burial and compromise:  753     0.0369226
Two-sided:              3882    0.19035
Other coalition strats: 90      0.00441306
==========================================
Manipulable elections:  16416   0.804943

and the higher number of voters, comparing to Smith//IRV:

Impartial culture, three candidtes, 97 voters, 50k elections, 32k tests 
per election:

CTE-Borda:

Burial, no compromise:  737     0.01474
Compromise, no burial:  4346    0.08692
Burial and compromise:  0       0
Two-sided:              15674   0.31348
Other coalition strats: 29192   0.58384
==========================================
Manipulable elections:  49949   0.99898

Smith//IRV:

Burial, no compromise:  1682    0.03364
Compromise, no burial:  4382    0.08764
Burial and compromise:  0       0
Two-sided:              0       0
Other coalition strats: 1866    0.03732
==========================================
Manipulable elections:  7930    0.1586

fpA - fpC:

Burial, no compromise:  3404    0.06808
Compromise, no burial:  4392    0.08784
Burial and compromise:  0       0
Two-sided:              779     0.01558
Other coalition strats: 0       0
==========================================
Manipulable elections:  8575    0.1715

Five candidates, 97 voters, 50k elections, 32k tests per election:

CTE-Borda:

Burial, no compromise:  838     0.01676
Compromise, no burial:  11720   0.2344
Burial and compromise:  522     0.01044
Two-sided:              9754    0.19508
Other coalition strats: 27166   0.54332
==========================================
Manipulable elections:  50000   1

Smith//IRV:

Burial, no compromise:  3407    0.06814
Compromise, no burial:  10961   0.21922
Burial and compromise:  1490    0.0298
Two-sided:              2       4e-05
Other coalition strats: 7904    0.15808
==========================================
Manipulable elections:  23764   0.47528

Here's a burial example with 13 voters:

2: A > B > C
4: A > C > B
1: B > A > C
4: C > A > B
2: C > B > A

A is the CW and wins. (The Borda order is A>C>B.) Then

2: A > B > C
4: A > C > B
1: B > A > C
4: C > B > A <-- was C > A > B
2: C > B > A

and C wins.

The Borda order is C>A>B and we have an ACBA cycle, the pairwise sort 
step swaps C and A; B is the loser and is eliminated, taking down A with 
it. So the problem seems to be that if either A or the candidate who 
beats A pairwise is the Borda loser, or can be made into the Borda 
loser, then burial pays.

-km