<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><div>On 25.6.2012, at 4.50, Michael Ossipoff wrote:</div><div><br></div><blockquote type="cite"><div class="gmail_quote"><blockquote style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0.8ex; padding-left: 1ex; border-left-color: rgb(204, 204, 204); border-left-width: 1px; border-left-style: solid; position: static; z-index: auto; " class="gmail_quote">Do you have an exact formulation on what you think is the crucial property that makes SL optimal or best in "equal representation" that all should follow (at least when compared to LR)? You focus very much on optimization of seats per quota, although you also agree that not even SL does perfect job here.</blockquote>
<div> </div><div>So what if SL isn't optimal for equality of S/Q? It does dramatically better than LR in that regard, and that's sufficient for this discussion.</div><div> </div><div>You ask for an exact formulation of the crucial property that makes SL [not optimal, but better than LR] in equal representation for people.</div></div></blockquote><div><br></div><div>Ok, that's a good definition. There is no "SL's optimal proportionality" and it is not "optmal for equality of S/Q" but to you it is important that it is better in S/Q than LR.</div><div><br></div><blockquote type="cite"><div class="gmail_quote"><blockquote style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0.8ex; padding-left: 1ex; border-left-color: rgb(204, 204, 204); border-left-width: 1px; border-left-style: solid; position: static; z-index: auto; " class="gmail_quote">I guess we have already agreed to disagree on the optimality of SL</blockquote>
<div> </div><div>[endquote]</div><div> </div><div> No we don't. I said that SL isn't optimal. But SL is nevertheless better than LR, when it comes to respecting people's right to equal representation.</div></div></blockquote><div><br></div>Ok, we agree to disagree on the (universal) "optimality of SL over LR" (and we agree that SL is not optimal in all aspects).</div><div><br></div><div><blockquote type="cite"><div class="gmail_quote"><div>In your above-quoted sentence, you claim that a full Hare quota of voters has no representation in district A (in my example).</div></div></blockquote><div><br></div><div>With "full Hare quota" I of course referred to my example that I copy below.</div><div><br></div><div><div><blockquote type="cite"><blockquote type="cite">Let's say we have proportions 61-13-13-13. SL allocates the seats 2-1-1-1. The number of quotas of each district/party has is 3.05 - 0.65 - 0.65 - 0.65. The third full quota of the largest district/party does not get its seat. Shouldn't all quotas get their representation?<br></blockquote></blockquote></div><div><br></div></div><blockquote type="cite"><div class="gmail_quote"><div>Do you think that's how allocation should be done?<br></div><div>[endquote]</div><div> </div><div>Yes.</div></div></blockquote><div><br></div><div>Ok, undesrstood. I guess this is another point where we agree to disagree. I think it is quite easy to end up in setting a requirement that in order to get good proportionality at least all full quotas should get a seat (and the small differences between different allocation methods shoud be only in how they allocate the remaining fragments of quota).</div><div><br></div><div>Although SL fails this criterion, it does not mean that SL would be a bad method. It is one of the best despite of violating this basic rule in some special (not common) situations. I just picked this example up to demonstrate that the monotonicity with respect to seats that divisor methods achieve leads to some disturbance in some other properties.</div><div><br></div><div>Juho</div><div><br></div><div><br></div><div><br></div><div><br></div></div></body></html>