<html><head></head><body><div style="color:#000; background-color:#fff; font-family:Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:13px"><div><span></span></div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1498319937379_7876">Given the possibility of a Condorcet paradox, the will of the majority becomes an incoherent notion. If A is preferred by a majority to B, then in a two-candidate election, then A should win under a majority system. But introduce candidate C, and B could end up winning, even though by majority logic, A is a better candidate than B.</div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1498319937379_7883"><br></div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1498319937379_7985">Obviously you know all about Condorcet paradoxes, but if you think that the majority criterion is some sort of absolute, then you are left with no option but to say that in some elections, A is a better winner than B, B a better winner than C, and C a better winner than A. And this makes no sense.</div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1498319937379_7904"><br></div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1498319937379_7918">You can also end up with winners hardly anyone wants. If there are two polarising candidates each with strong support and a complete unknown, you could have the following ballots:</div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1498319937379_7931"><br></div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1498319937379_7932">49 voters: A>C>B</div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1498319937379_7933">49 voters: B>C>A</div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1498319937379_7934">2 voters: C>A>B</div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1498319937379_7935"><br></div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1498319937379_7953">It could be that the score ballots (out of 10) would be:</div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1498319937379_7952"><br></div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1498319937379_7936">49: A=10, C=1, B=0</div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1498319937379_7944">49: B=10, C=1, A=0</div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1498319937379_7954">2: C=2, A=1, B=0</div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1498319937379_7973"><br></div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1498319937379_8004" dir="ltr">C is the Condorcet winner.</div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1498319937379_7974"><br></div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1498319937379_7976" dir="ltr">There's no way I'd accept that a C victory is the best result because of blind adherence to some sort of majority principle under all circumstances. This is not to say that Condorcet methods are necessarily bad, but just that there are elections when they would produce what I would consider to be the wrong result. And in this situation, very wrong.</div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1498319937379_7983" dir="ltr"><br></div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1498319937379_7984" dir="ltr">Toby<br id="yui_3_16_0_ym19_1_1498319937379_7897"><br></div><div class="yahoo_quoted" id="yui_3_16_0_ym19_1_1498319937379_7805" style="display: block;"> <div id="yui_3_16_0_ym19_1_1498319937379_7804" style="font-family: Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 13px;"> <div id="yui_3_16_0_ym19_1_1498319937379_7803" style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 16px;"> <div id="yui_3_16_0_ym19_1_1498319937379_7843" dir="ltr"> <font id="yui_3_16_0_ym19_1_1498319937379_7842" face="Arial" size="2"> <hr size="1" id="yui_3_16_0_ym19_1_1498319937379_7851"> <b><span style="font-weight: bold;">From:</span></b> robert bristow-johnson <rbj@audioimagination.com><br> <b><span style="font-weight: bold;">To:</span></b> election-methods@electorama.com <br> <b id="yui_3_16_0_ym19_1_1498319937379_7850"><span id="yui_3_16_0_ym19_1_1498319937379_7849" style="font-weight: bold;">Sent:</span></b> Saturday, 24 June 2017, 3:52<br> <b><span style="font-weight: bold;">Subject:</span></b> Re: [EM] The election methods trade-off paradox/impossibility theorems paradox.<br> </font> </div> <div class="y_msg_container" id="yui_3_16_0_ym19_1_1498319937379_7802"><br><div id="yiv9018425364"><div id="yui_3_16_0_ym19_1_1498319937379_7801"><div id="yui_3_16_0_ym19_1_1498319937379_7800"><br clear="none">
</div><div id="yui_3_16_0_ym19_1_1498319937379_7819">no. the goal of a voting system in a democracy is to determine, reflect, and implement the will of the majority of citizens, all with equal franchise. letting a minority rule sets up all sorts of incentive for strategic voting.<br clear="none"></div></div></div><br><br></div> </div> </div> </div></div></body></html>