<div dir="ltr"><div dir="ltr"><div class="gmail_default" style="font-family:trebuchet ms,sans-serif;font-size:small"><br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sun, Jan 9, 2022 at 4:41 PM Kristofer Munsterhjelm <<a href="mailto:km_elmet@t-online.de">km_elmet@t-online.de</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">> I couldn't figure out how to decide which voters need to be in the<br>
> coalition or what ballot they need to cast to maximize their chances.<br>
<br>
In quadelect (my election simulator), I just do this:<br>
<br>
for n = 1...numiters:<br>
e_A = sample a random v-voter c-candidate election according to some<br>
given distribution<br>
w_A = winner of e_A according to method M<br>
for c_k in every candidate but w_A:<br>
for i = 1...strategy_iters:<br>
e_B = e_A<br>
for every ballot B in e_B:<br>
if B ranks c_k ahead of w_A:<br>
replace B with a random preference order<br>
w_B = winner of e_B according to method M<br>
if w_B = c_k:<br>
then strategy successful<br>
if strategy successful:<br>
increment number of strategy successes SS<br>
else:<br>
increment number of strategy failures SF<br>
<br>
strategic susceptibility = SS/(SS+SF)<br>
<br>
It underestimates susceptibility with large numbers of voters but should<br>
give approximately the same results as JGA with his orders of magnitude.<br></blockquote><div><br></div><div><div class="gmail_default" style="font-family:"trebuchet ms",sans-serif;font-size:small">Hmm... The numbers I'm getting are a lot smaller than those in the paper. I'm using Benham, V=99, N=1, C=6 and the voters and candidates follow a standard normal, just as in the paper. I chose those parameters because Table 1 gives a strategic susceptibility of 0.622 which should be easy to detect, but I'm only getting 0.00196; so off by over two orders of magnitude. I don't have as many iterations (numiter = 100, strategy_iters = 100) but that should not change the overall scale.</div><div class="gmail_default" style="font-family:"trebuchet ms",sans-serif;font-size:small"><br></div><div class="gmail_default" style="font-family:"trebuchet ms",sans-serif;font-size:small">It's hard to see how randomly shuffling ballots would be a strategy. I tried changing the strategy: after the random ballot is generated, candidate c_k is moved to the top and w_A to the bottom. That simple strategy increases the susceptibility to 0.0785, but that's still one order of magnitude off from the paper.</div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><a href="https://electowiki.org/wiki/Raynaud" rel="noreferrer" target="_blank">https://electowiki.org/wiki/Raynaud</a> suggests that all versions of<br>
Raynaud pass ISDA, including Raynaud(GL). I agree, it would be useful to<br>
have a table, but it wouldn't be practical to render it for all criteria<br>
defined on electowiki; it would need some kind of interactive component<br>
so you could select just the criteria (and methods) that interest you.<br></blockquote><div><br></div><div><div class="gmail_default" style="font-family:"trebuchet ms",sans-serif;font-size:small">I shouldn't get distracted with this right now, but maybe in a few months I could make a Google spreadsheet --- a poor man's interactive database.</div></div><div class="gmail_default" style="font-family:"trebuchet ms",sans-serif;font-size:small"><br></div></div>-- <br><div dir="ltr" class="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><font face="trebuchet ms, sans-serif">Dr. Daniel Carrera</font></div><div dir="ltr"><font face="trebuchet ms, sans-serif">Postdoctoral Research Associate</font></div><div><font face="trebuchet ms, sans-serif">Iowa State University</font></div></div></div></div></div></div></div></div></div></div></div>