<div dir="ltr"><div dir="ltr"><div class="gmail_default" style="font-family:trebuchet ms,sans-serif;font-size:small"><br></div></div><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Mon, Jan 17, 2022 at 4:29 AM Colin Champion <colin.champion@routemaster.app> 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">
<div>On the magnitude of errors, my own figures suggest that
Condorcet/Hare makes fewer but larger errors than minimax when
confronted with false cycle tactics, and therefore looks marginally
better in terms of accuracy (and no doubt much better in terms of
strategy resistance) but significantly worse in terms of Euclidean
loss. See<br>
<a href="http://www.masterlyinactivity.com/condorcet/condorcet.html#results" target="_blank">http://www.masterlyinactivity.com/condorcet/condorcet.html#results</a><br>
(where Condorcet/Hare=Condorcet+AV).<br></div></blockquote><div><br></div><div><br></div><div><div class="gmail_default" style="font-family:"trebuchet ms",sans-serif;font-size:small">Thanks for the link. I'm going to need time to digest all of that. I just updated my program to compute the Eucledian loss. I'm sure I can't compare my numbers to yours; there will be a lot of implementation differences, and you implement a lot more strategies than I do. But here it goes anyway:</div></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">Method , suscep, new winner is ...<br>MiniMax , 0.412 , better=0.134, worse=0.866<br>Hare , 0.066 , better=0.655, worse=0.345<br>Benham , 0.047 , better=0.135, worse=0.865<br>Smith_IRV, 0.047 , better=0.120, worse=0.880<br>Range , 0.787 , better=0.072, worse=0.928<br>STAR , 0.750 , better=0.061, worse=0.939<br></div><div><br></div><div><br></div><div><div class="gmail_default" style="font-family:"trebuchet ms",sans-serif;font-size:small">The first column ("suscep") is how often the method is susceptible to strategy. It's basically the same number I've been posting here lately. The next two numbers tell you how often the new winner (i.e. after strategy) is better (i.e. smaller Eucledian distance to the mean voter) or worse than the original winner. I was surprised to see that with Hare / IRV tactical voting actually seems to make candidates better. I wonder how many of those would be similar to the centre squeeze scenario you were just telling me about. For other methods, strategy seems to be universally unhelpful.</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">Here is the Eucledian loss (gain?) for each case:</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">Method , Change in Eucledian distance<br>MiniMax , better=0.067, worse=0.196<br>Hare , better=0.157, worse=0.172<br>Benham , better=0.081, worse=0.228<br>Smith_IRV, better=0.081, worse=0.241<br>Range , better=0.077, worse=0.355<br>STAR , better=0.068, worse=0.335<br></div><br></div><div><div class="gmail_default" style="font-family:"trebuchet ms",sans-serif;font-size:small">The units are a bit different from yours. The mean voter is at a distance ~2.0 from the center, and ditto for candidates. Overall, these don't look like very big jumps in either direction. That said, for all systems except Hare, the downside of using strategy is significantly greater than the upside.</div><div class="gmail_default" style="font-family:"trebuchet ms",sans-serif;font-size:small"><br></div></div><div class="gmail_default" style="font-family:"trebuchet ms",sans-serif;font-size:small">You said that Condorcet/Hare makes fewer but larger errors than minimax when confronted with false cycle tactics. I cannot confirm that because I have not implemented false cycle tactics. But for the strategies I have implemented, they look pretty similar.</div><div class="gmail_default" style="font-family:"trebuchet ms",sans-serif;font-size:small"><br></div></div><div><div class="gmail_default" style="font-family:"trebuchet ms",sans-serif;font-size:small">Cheers</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>