<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; ">Meek's method elects A, C1 & C2 in this example.<DIV><BR><DIV><DIV>On Apr 19, 2007, at 10:18 AM, <A href="mailto:raphfrk@netscape.net">raphfrk@netscape.net</A> wrote:</DIV><BR class="Apple-interchange-newline"><BLOCKQUOTE type="cite"> <DIV> I was thinking about an easier <SPAN class="correction" id="">solution</SPAN> to the vote management problem. <BR> This is where it is sometimes in a party's interests to try to split their support<BR> equally between two candidate due to exhausted ballots. In effect, they <BR> get a candidate elected without a quota.<BR> <BR> For example, assume a 3 seat election and 4 candidates.<BR> <BR> 12500: A<BR> 9000: B<BR> 18500: (<SPAN class="correction" id="">C1</SPAN>,<SPAN class="correction" id="">C2</SPAN>)<BR> <BR> Voters might vote<BR> <BR> 12500: A<BR> 9000: B><SPAN class="correction" id="">C1</SPAN>><SPAN class="correction" id="">C2</SPAN>>A<BR> 12000: <SPAN class="correction" id="">C1</SPAN>><SPAN class="correction" id="">C2</SPAN><BR> 6500: <SPAN class="correction" id="">C2</SPAN>><SPAN class="correction" id="">C1</SPAN><BR> <BR> Quota is 10000 (<SPAN class="correction" id="">approx</SPAN>)<BR> <BR> Round 1: A is elected, all his votes are <SPAN class="correction" id="">exhasted</SPAN><BR> A: 12500 *<BR> B: 9000<BR> C:1 12000<BR> C2: 6500<BR> <BR> Round 2: C1 is elected and votes transfer to C2<BR> <BR> A: 10000*<BR> B: 9000<BR> </DIV> <DIV><SPAN class="correction" id="">C1</SPAN>: 10000*<BR> <SPAN class="correction" id="">C2</SPAN>: 8500<BR> <BR> B then wins the last seat as <SPAN class="correction" id="">C2</SPAN> is eliminated.<BR> <BR> However, if <SPAN class="correction" id="">C1</SPAN> and <SPAN class="correction" id="">C2</SPAN> had evenly split their 18500 votes, they would have won both <BR> seats as they would have had 9250 votes each and B would have been eliminated first. <BR> This causes parties to participate in 'vote management', the effect of which is that it is <BR> no longer tactically correct to just rank the candidates in order of your choice.<BR> <BR> The best solution would be to re-calculate the quota after each round. However, this <BR> would greatly complicate the counting process (especially if it was hand counted).<BR> <BR> However, really all that is needed is to recalculate the quota once at the end. <BR> <BR> The rule would activate when<BR> a) there is no candidate with a surplus to distribute<BR> b) the number of <SPAN class="correction" id="">uneliminated</SPAN> candidates is one greater than the seats to allocate<BR> <BR> The quota is recalculated and surplus transferred to one of the remaining<BR> 2 unelected candidates.<BR> <BR> Round 3 would change to:<BR> <BR> Quota recalculated: (10000+9000+10000+8500)/4=9375<BR> <BR> A: 9375 (transfers 625 and they exhaust)<BR> B: 9000 (below quota)<BR> <SPAN class="correction" id="">C1</SPAN>: 9375 (transfers 625 to <SPAN class="correction" id="">C2</SPAN>)<BR> <SPAN class="correction" id="">C2</SPAN>: 9125 (625 transferred in)<BR> <BR> Ideally, this should be repeated until it converges. In fact, it is probably<BR> relatively easy to work out mathematically what the final result would be<BR> without actually counting the additional rounds.<BR> <BR> Anyway, the result is that C2 has more votes than B and is thus elected. This<BR> eliminates the tactical benefit to voters who participate in vote management, <BR> which allows them to be honest. It has the additional benefit that all elected<BR> candidates represent the same number of voters (at least all the ones who <BR> come from the same district).<BR> <BR> </DIV> <DIV style="clear: both;"><SPAN class="correction" id="">Raphfrk</SPAN><BR> --------------------<BR> Interesting site<BR> "what if anyone could modify the laws"<BR> <BR> <SPAN class="correction" id="">www</SPAN>.<SPAN class="correction" id="">wikocracy</SPAN>.<SPAN class="correction" id="">com</SPAN></DIV> <DIV> </DIV> <DIV class="AOLPromoFooter"> <HR style="margin-top:10px;"> <A href="http://pr.atwola.com/promoclk/100122638x1081283466x1074645346/aol?redir=http%3A%2F%2Fwww%2Eaim%2Ecom%2Ffun%2Fmail%2F" target="_blank"><B>Check Out the new free AIM(R) Mail</B></A> -- 2 GB of storage and industry-leading spam and email virus protection.<BR> </DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">----</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">election-methods mailing list - see <A href="http://electorama.com/em">http://electorama.com/em</A> for list info</DIV> </BLOCKQUOTE></DIV><BR></DIV></BODY></HTML>