<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><div>On 12.2.2013, at 1.24, Jameson Quinn wrote:</div><div><br></div><blockquote type="cite"><div class="gmail_quote">2013/2/11 Kristofer Munsterhjelm <span dir="ltr"><<a href="mailto:km_elmet@lavabit.com" target="_blank">km_elmet@lavabit.com</a>></span><br></div></blockquote><div><br></div><blockquote type="cite"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0.8ex; border-left-width: 1px; border-left-color: rgb(204, 204, 204); border-left-style: solid; padding-left: 1ex; position: static; z-index: auto; ">(Also, speaking of criteria: if I had enough time, I would try to find a monotone variant of Schulze STV. I think one can make monotone Droop-proportional multiwinner methods, since I made a Bucklin hack that seemed to be both monotone and Droop-proportional. However, I have no mathematical proof that the method obeys both criteria.)</blockquote>
<div><br></div><div>What does monotone even mean for PR? You can make something that's sequentially monotone, but it's (I think) impossible to avoid situations where AB were winning but changing C>A>B to A>B>C causes B to lose (or variants of this kind of problem). That's still technically "monotone", but from a voters perspective, it's not usefully so.</div></div></blockquote><div><br></div><div>I think monotonicity is sometimes an obvious requirement but not always. A ranked ordering (=> monotonicity with respect to adding seats) may give different results than a proportional algorithm that just picks the agreed number of representatives (with no order). Sometimes a ranked ordering is needed (like in the Czech Green Party canddidate list), sometimes not. The need to establish a ranked order may make the proportionality of the results slightly worse.</div><div><br></div><div>I also like the Alabama paradox in the sense that one can as well consider such results the correct and exact outcome, not a "negative paradox". All in all, both appraches are needed, for different needs.</div><div><br></div></div>Juho<div><br></div><div><br></div><div><br></div></body></html>