<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; ">Dear Election Methods,<DIV><BR class="khtml-block-placeholder"></DIV><DIV>The fact that Largest Remainder (Hamilton) violates "house monotonicity" (e.g. Alabama Paradox) is less serious for apportioning the US House of Representatives now that it has a fixed size of 435 than the fact that it violates "population monotonicity." (See the book about apportionment by Balinski and Young.) All of the so-called divisor methods are population and house monotone but can violate the condition of obeying quota (e.g. if one takes the product of the percent population for a state and the house size, one would like the number of seats given to a state to be either that number if it is an integer or the integer just larger or small than that number if it is not an integer). The Balinski-Young Theorem basically shows that one can not have a method that both obeys quota and is population monotone.</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Cheers,</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Joe</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV> </DIV><DIV> </DIV><DIV><BR><DIV><DIV>On Dec 6, 2006, at 1:58 PM, Juho wrote:</DIV><BR class="Apple-interchange-newline"><BLOCKQUOTE type="cite"><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">On Dec 6, 2006, at 4:33 , MIKE OSSIPOFF wrote:</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV> <BLOCKQUOTE type="cite"><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">There was later another bill to enact</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">LR/Hamilton. It passed and wasn't vetored, and LR/Hamilton was used <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">for a</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">while--till someone pointed out the bizarre paradoxes that it's <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">subject to:</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Some people move from another staste to your state, causing your <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">state to</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">lose a seat. We add a seat to the House, and that causes your state <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">to lose</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">a seat. When that was pointed out, LR/Hamilton was immediately <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">repealed and</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">discarded. (IRVists please take note).</DIV> </BLOCKQUOTE><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">I understand that LR/Hamilton may lead to the Alabama paradox and <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">people may dislike LR/Hamilton because of this. But I think LR/<SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Hamilton is quite proportional and unbiased. Are there other reasons <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">why LR/Hamilton is not favoured? SL/Webster is close to LR/Hamilton <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">and avoids the Alabama paradox, but LR/Hamilton might still be <SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">considered more exact in providing proportionality.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Juho Laatu</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Send instant messages to your online friends <A href="http://uk.messenger.yahoo.com">http://uk.messenger.yahoo.com</A><SPAN class="Apple-converted-space"> </SPAN></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> <SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 16px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><DIV><BR class="khtml-block-placeholder"></DIV><DIV>------------------------------------------------</DIV><DIV>Joseph Malkevitch</DIV><DIV>Department of Mathematics</DIV><DIV>York College (CUNY)</DIV><DIV>Jamaica, New York 11451</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Phone: 718-262-2551 (Voicemail available)</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>My new email is:</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV><A href="mailto:malkevitch@york.cuny.edu">malkevitch@york.cuny.edu</A></DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>web page:</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV><A href="http://www.york.cuny.edu/~malk">http://www.york.cuny.edu/~malk</A></DIV><DIV><BR class="khtml-block-placeholder"></DIV><BR class="Apple-interchange-newline"></SPAN></SPAN></SPAN></SPAN></SPAN> </DIV><BR></DIV></BODY></HTML>