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<p>Kristofer,<br>
</p>
<p>
<blockquote type="cite">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).
<br>
<br>
My implementation uses bubble sort, which I understand is the
same as sink sort (see e.g.
<a class="moz-txt-link-freetext" href="https://xlinux.nist.gov/dads/HTML/sinkSort.html">https://xlinux.nist.gov/dads/HTML/sinkSort.html</a>). 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.
</blockquote>
<br>
The definition of "sink sort" includes (from the link you gave):<br>
<blockquote type="cite"><strong
style="color: rgb(0, 0, 0); font-family: Verdana, Arial, Helvetica, sans-serif; font-size: medium; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: normal; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;">Definition:</strong><span
style="color: rgb(0, 0, 0); font-family: Verdana, Arial, Helvetica, sans-serif; font-size: medium; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: normal; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;"><span> </span>Sort
by comparing each adjacent pair of items in a<span> </span></span><a
href="https://xlinux.nist.gov/dads/HTML/list.html"
style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: medium; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: normal; background-color: rgb(255, 255, 255);"><em>list</em></a><span
style="color: rgb(0, 0, 0); font-family: Verdana, Arial, Helvetica, sans-serif; font-size: medium; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: normal; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;"><span> </span>in
turn, swapping the items if necessary...</span></blockquote>
<br>
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.<br>
<br>
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.<br>
<br>
The choice of one over the other seems arbitrary to me. <br>
<br>
The concise (i.e. minus the redundant preamble) definition given
by Forest of this "Duncan" method suggestion is <br>
<blockquote type="cite">
<pre
style="white-space: pre-wrap; color: rgb(0, 0, 0); font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;">..elect the highest score candidate that pairbeats every candidate
with lower score.</pre>
</blockquote>
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<br>
or Margins-Sorted Borda.<br>
<br>
Believe it or not, it is simply "elect the Smith-set member with
the lowest Borda score".<br>
<br>
(Someone please correct me if I have that wrong.)<br>
<br>
Chris B.<br>
<br>
</p>
<div class="moz-cite-prefix">On 14/10/2023 9:51 pm, Kristofer
Munsterhjelm wrote:<br>
</div>
<blockquote type="cite"
cite="mid:7b4946e5-5da8-760b-76e3-29123035dd20@t-online.de">On
10/13/23 19:11, Forest Simmons wrote:
<br>
<blockquote type="cite">Dear EM List Friends,
<br>
<br>
We need your feedback on this draft of a proposal before we
submit a version of it to the voting reform community at large.
<br>
</blockquote>
<br>
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).
<br>
<br>
My implementation uses bubble sort, which I understand is the same
as sink sort (see e.g.
<a class="moz-txt-link-freetext" href="https://xlinux.nist.gov/dads/HTML/sinkSort.html">https://xlinux.nist.gov/dads/HTML/sinkSort.html</a>). 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.
<br>
<br>
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.
<br>
<br>
Here are the stats:
<br>
<br>
Impartial culture, three candidates, 13 voters, 25k elections, 32k
tests per election:
<br>
<br>
CTE-Borda:
<br>
<br>
Burial, no compromise: 5381 0.21524
<br>
Compromise, no burial: 2050 0.082
<br>
Burial and compromise: 0 0
<br>
Two-sided: 5085 0.2034
<br>
Other coalition strats: 4120 0.1648
<br>
==========================================
<br>
Manipulable elections: 16636 0.66544
<br>
<br>
For comparison, Schulze:
<br>
<br>
Burial, no compromise: 9988 0.426582
<br>
Compromise, no burial: 210 0.00896899
<br>
Burial and compromise: 282 0.0120441
<br>
Two-sided: 2206 0.0942171
<br>
Other coalition strats: 0 0
<br>
==========================================
<br>
Manipulable elections: 12686 0.541813
<br>
<br>
Impartial culture, five candidates, 13 voters, 25k elections, 32k
tests per election:
<br>
<br>
CTE-Borda:
<br>
<br>
Burial, no compromise: 8654 0.34616
<br>
Compromise, no burial: 3864 0.15456
<br>
Burial and compromise: 2054 0.08216
<br>
Two-sided: 6673 0.26692
<br>
Other coalition strats: 2032 0.08128
<br>
==========================================
<br>
Manipulable elections: 23277 0.93108
<br>
<br>
Schulze again:
<br>
<br>
Burial, no compromise: 11196 0.548985
<br>
Compromise, no burial: 495 0.0242718
<br>
Burial and compromise: 753 0.0369226
<br>
Two-sided: 3882 0.19035
<br>
Other coalition strats: 90 0.00441306
<br>
==========================================
<br>
Manipulable elections: 16416 0.804943
<br>
<br>
and the higher number of voters, comparing to Smith//IRV:
<br>
<br>
Impartial culture, three candidtes, 97 voters, 50k elections, 32k
tests per election:
<br>
<br>
CTE-Borda:
<br>
<br>
Burial, no compromise: 737 0.01474
<br>
Compromise, no burial: 4346 0.08692
<br>
Burial and compromise: 0 0
<br>
Two-sided: 15674 0.31348
<br>
Other coalition strats: 29192 0.58384
<br>
==========================================
<br>
Manipulable elections: 49949 0.99898
<br>
<br>
Smith//IRV:
<br>
<br>
Burial, no compromise: 1682 0.03364
<br>
Compromise, no burial: 4382 0.08764
<br>
Burial and compromise: 0 0
<br>
Two-sided: 0 0
<br>
Other coalition strats: 1866 0.03732
<br>
==========================================
<br>
Manipulable elections: 7930 0.1586
<br>
<br>
fpA - fpC:
<br>
<br>
Burial, no compromise: 3404 0.06808
<br>
Compromise, no burial: 4392 0.08784
<br>
Burial and compromise: 0 0
<br>
Two-sided: 779 0.01558
<br>
Other coalition strats: 0 0
<br>
==========================================
<br>
Manipulable elections: 8575 0.1715
<br>
<br>
Five candidates, 97 voters, 50k elections, 32k tests per election:
<br>
<br>
CTE-Borda:
<br>
<br>
Burial, no compromise: 838 0.01676
<br>
Compromise, no burial: 11720 0.2344
<br>
Burial and compromise: 522 0.01044
<br>
Two-sided: 9754 0.19508
<br>
Other coalition strats: 27166 0.54332
<br>
==========================================
<br>
Manipulable elections: 50000 1
<br>
<br>
Smith//IRV:
<br>
<br>
Burial, no compromise: 3407 0.06814
<br>
Compromise, no burial: 10961 0.21922
<br>
Burial and compromise: 1490 0.0298
<br>
Two-sided: 2 4e-05
<br>
Other coalition strats: 7904 0.15808
<br>
==========================================
<br>
Manipulable elections: 23764 0.47528
<br>
<br>
Here's a burial example with 13 voters:
<br>
<br>
2: A > B > C
<br>
4: A > C > B
<br>
1: B > A > C
<br>
4: C > A > B
<br>
2: C > B > A
<br>
<br>
A is the CW and wins. (The Borda order is A>C>B.) Then
<br>
<br>
2: A > B > C
<br>
4: A > C > B
<br>
1: B > A > C
<br>
4: C > B > A <-- was C > A > B
<br>
2: C > B > A
<br>
<br>
and C wins.
<br>
<br>
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.
<br>
<br>
-km
<br>
</blockquote>
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