<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; ">Dear Election List,<DIV><BR class="khtml-block-placeholder"></DIV><DIV>The issue of whether or not a particular method of apportionment is biased is rather complex it seems to me. Although I greatly respect the work of Balinski and Young I do not find the discussion they have about bias totally compelling. (Look at the diagram on page 72 of the revised edition of their book to see data for the apportionment of the House of the Representative using the Balinski-Young measure of bias.) One problem for me is that the Constitution requires that each state get one seat. Thus, a state can get a set even if in some sense it might not be entitled to this in a pairwise comparison framework. The Constitution gives small (and large) states one seat automatically. Thus, it seems to me that one has to "sort out" the effects due to the Constitutional requirement of 1 seat for each state and the effects of the method of apportionment. Balinski and Young do take this issue into account but it is not clear to me if their way is the only reasonable one. In the year 2000, Huntington-Hill and Webster gave the same apportionment. In 1990, they differed with regard to 1 seat between two states. (Webster gave one more seat to MA. at the expense of Oklahoma, and Huntington-Hill the other other way around.)</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Best,</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Joe</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV><BR><DIV><DIV>On Dec 8, 2006, at 2:29 PM, MIKE OSSIPOFF wrote:</DIV><BR class="Apple-interchange-newline"><BLOCKQUOTE type="cite"><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 accidentally said that Hill has "unbias". I meant to say that it has bias.</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; ">Mike Ossipoff</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; ">p.s. Right now is close to the anniversary of the date when Webster was<SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">replaced by Hill, for apportioning the House.</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; ">_________________________________________________________________</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Stay up-to-date with your friends through the Windows Live Spaces friends<SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">list.<SPAN class="Apple-converted-space"> </SPAN></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><A href="http://clk.atdmt.com/MSN/go/msnnkwsp0070000001msn/direct/01/?href=http://spaces.live.com/spacesapi.aspx?wx_action=create&wx_url=/friends.aspx&mk">http://clk.atdmt.com/MSN/go/msnnkwsp0070000001msn/direct/01/?href=http://spaces.live.com/spacesapi.aspx?wx_action=create&wx_url=/friends.aspx&mk</A></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; ">----</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>