<html><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif;font-size:13px"><div>From: Kristofer Munsterhjelm <<a href="mailto:km_elmet@t-online.de">km_elmet@t-online.de</a>><br></div><div id="yui_3_16_0_1_1412534331220_3660"><br>>That sounds like house monotonicity. I don't know if my example is <br>>translatable to Approval voting, but this left-right-center example <br>>seems to show that it's not always desirable for ranked voting. E.g. <br>>something like:</div><div id="yui_3_16_0_1_1412534331220_3659">>43: L>C>R<br>>34: R>C>L<br>>12: C>R>L</div><div id="yui_3_16_0_1_1412534331220_3658">>If you have one seat, then C is a compromise candidate, doesn't give too <br>>much bias to either the left or right wing, and thus provides <br>>proportionality. But in the two-seat case, balance comes from electing L <br>>and R; LC would bias to the left and RC would bias to the right.</div><div id="yui_3_16_0_1_1412534331220_3657">>For this case, let L "really" be L1, L2, L3, ..., Ln; and the same with <br>>C and R. That means the ballots are really L1 > L2 > L3 > ... > Ln > C1 <br>> > C2 > ..., etc.</div><div id="yui_3_16_0_1_1412534331220_3656">>So in the one-seat case:</div><div id="yui_3_16_0_1_1412534331220_3655">>L: 0 seats<br>>C: 1 seat<br>>R: 0 seats</div><div id="yui_3_16_0_1_1412534331220_3663">>(w = 0, x = 1) is preferable to</div><div id="yui_3_16_0_1_1412534331220_3647">>L: 1 seat w + 1<br>>C: 0 seats x - 1<br>>R: 0 seats</div><div id="yui_3_16_0_1_1412534331220_3648">>but in the 2-seat case:</div><div id="yui_3_16_0_1_1412534331220_3649">>L: 0 seats w = 0<br>>C: 1 seat x = 1<br>>R: 1 seat</div><div id="yui_3_16_0_1_1412534331220_3664">>is not preferable to</div><div id="yui_3_16_0_1_1412534331220_3665">>L: 1 seat w + 1<br>>C: 0 seats x - 1<br>>R: 1 seat.</div><div id="yui_3_16_0_1_1412534331220_3666">>You could argue that these are "entangled" factions (each group of <br>>voters ranks all the candidates, not just those he supports). But then <br>>you might have to clarify it to say that it doesn't hold in the case of <br>>entangled factions.</div><div id="yui_3_16_0_1_1412534331220_3667"><br></div><div id="yui_3_16_0_1_1412534331220_3681" dir="ltr">I suppose the discussion had gone down the line of party list voting, and not even approval voting, let alone ranked ballots, so yes, I'd have to consider exactly what would make sense for entangled ballots.<br></div></div></body></html>