[EM] Fwd: Duncan Proposal Draft

Sat Oct 14 09:10:44 PDT 2023

Kristofer,

> 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. 

The definition of "sink sort" includes (from the link you gave):
> *Definition:*Sort by comparing each adjacent pair of items in a/list/ 
> <https://xlinux.nist.gov/dads/HTML/list.html>in turn, swapping the 
> items if necessary...

As I understand the items in the list are in order of whatever (in this 
case Borda count) with the highest-ordered at the top of the list.

Sink sort starts at the top and "sinks" down it, while "bubble" sort 
starts at the bottom and moves up  (the same direction as bubbles in 
water) it.

The choice of one over the other seems arbitrary to me.

The concise (i.e. minus the redundant preamble) definition given by 
Forest of this "Duncan" method suggestion is
> ..elect the highest score candidate that pairbeats every candidate
> with lower score.
I'm not sure of the exact definition of "CTE-Borda" but I don't think 
Duncan is the same thing.  Nor is it Sink-Sorted Borda  or Bubble-Sorted 
Borda
or Margins-Sorted Borda.

Believe it or not, it is simply  "elect the Smith-set member with the 
lowest Borda score".

(Someone please correct me if I have that wrong.)

Chris B.

On 14/10/2023 9:51 pm, Kristofer Munsterhjelm wrote:
> 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
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