<html><body><div style="color:#000; background-color:#fff; font-family:times new roman, new york, times, serif;font-size:12pt"><div style="RIGHT: auto"><SPAN style="RIGHT: auto">Andy</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">Candidates can go up the rankings or down when a candidate is eliminated in IRV, and it's possible to do both in different rounds. A plurality winner could slip down and be eliminated in a case where they would have still gone up again and <VAR id=yui-ie-cursor></VAR>won had they not been eliminated. So:</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">30: A>B>C>D</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">26: B>A>C>D</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">24: C>A>B>D</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">10: D>B>A>C</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">10: D>C>A>B</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">Round 1:</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">A: 30<BR>B: 26<BR>C: 24<BR>D: 20</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">D eliminated</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">Round 2:</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">B: 36<BR>C: 34<BR>A: 30</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">A eliminated</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">Round 3:</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">B: 66<BR>C: 34</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">B wins the IRV election whereas A would have been the plurality winner and the (quite strong) Condorcet winner.</SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN> </div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto"></SPAN></div>
<div style="RIGHT: auto"><SPAN style="RIGHT: auto">A>B: 64-36<BR>A>C: 66-34<BR>A>D: 80-20</SPAN></div>
<div style="RIGHT: auto"><BR style="RIGHT: auto">Toby<BR></div>
<div style="RIGHT: auto"> </div>
<div style="RIGHT: auto"> </div>
<DIV style="FONT-FAMILY: times new roman, new york, times, serif; FONT-SIZE: 12pt">
<DIV style="FONT-FAMILY: times new roman, new york, times, serif; FONT-SIZE: 12pt"><FONT size=2 face=Arial>
<DIV style="BORDER-BOTTOM: #ccc 1px solid; BORDER-LEFT: #ccc 1px solid; PADDING-BOTTOM: 0px; LINE-HEIGHT: 0; MARGIN: 5px 0px; PADDING-LEFT: 0px; PADDING-RIGHT: 0px; HEIGHT: 0px; FONT-SIZE: 0px; BORDER-TOP: #ccc 1px solid; BORDER-RIGHT: #ccc 1px solid; PADDING-TOP: 0px" class=hr readonly="true" contenteditable="false"></DIV><B><SPAN style="FONT-WEIGHT: bold">From:</SPAN></B> Andy Jennings <elections@jenningsstory.com><BR><B><SPAN style="FONT-WEIGHT: bold">To:</SPAN></B> EM <election-methods@lists.electorama.com><BR><B><SPAN style="FONT-WEIGHT: bold">Sent:</SPAN></B> Saturday, 24 September 2011, 0:13<BR><B><SPAN style="FONT-WEIGHT: bold">Subject:</SPAN></B> [EM] Is there any profile where IRV is worse than Plurality?<BR></FONT><BR>
<DIV id=yiv347954381>Since we're discussing IRV quite a bit lately, here's a question:
<DIV><BR></DIV>
<DIV>- Is there any voter profile where IRV gives a worse result than plurality?</DIV>
<DIV><BR></DIV>
<DIV>I can't seem to think of one. So is it true that, mathematically, IRV dominates Plurality, that is IRV is always at least as good as plurality and sometimes strictly better?</DIV>
<DIV><BR></DIV>
<DIV><BR></DIV>
<DIV>Even if that is true, I still believe that IRV is harmful, socially. By successfully avoiding the traditional spoiler problem (where spoilers are very weak), it leads people to believe that it is immune to the spoiler problem. Then it leads them directly into the second-tier spoiler scenarios where a large group of voters will, by voting honestly, cause their least favorite candidate to win.</DIV>
<DIV><BR></DIV>
<DIV>~ Andy</DIV></DIV><BR>----<BR></DIV></DIV></div></body></html>