----------- Forwarded Letter ----------- From: Alejandro Solá <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]>, <[EMAIL PROTECTED]> Subject: The search for perfect STV, with ties allowed Date: Sat, 20 May 2000 18:07:06 -0400 I suggest the following system for multi-member elections. Please relay to the Elections Methods List and other interested parties. [ok] 1. Ballot paper 1.1. Whether on paper or on screen, the "ballot paper" lists the candidates in columns, one for each political party. Independents are listed on a separate column. Voters enter the number of their preference besides each candidate's name. I choose to call these "individual preferences" (ie, preferences for individual candidates). Up to now, exactly the same as in STV. 1.2. But at the bottom of each party's column, there is a slot for "all other candidates for this party". And at the very bottom of the ballot, there is a slot for "all other candidates". I choose to call these "collective preferences". The advantages of collective preferences, especially on very long ballots (such as those necessary in a single national constituency, which I advocate), are twofold: a) allows party voting for those voters who don't know candidates well enough; b) allows easy ranking of most disliked as well as most liked candidates. Simply mark your first preferences for the candidates you like most, then rank "all other candidates", and lastly rank those you like least. 1.3. Apart from the ties implied by collective preferences, candidates can indicate ties by ranking equally several preferences (individual and/or collective). Each tied entry is given an equal fraction of the vote. 1.3.1. Ties consisting exclusively of individual preferences are considered individual preferences. 1.3.2. Ties consisting wholly of individual preferences are considered collective preferences. 1.3.3. Ties including both individual and collective preferences are apportioned between individual and collective preferences. In these preferences, each individual and collective mark account for an equal fraction of the vote (ie, if it so appears, my entry for William Hague weighs the same as my same-ranked preference for "all other Labour Party candidates"). 1.3.4. Any individual preference tied with a collective preference including it (ie, the voter ranked equally Tony Blair and "all other Labour Party candidates") is "submerged" within the collective preference (ie, only the ranking for "all other Labour Party candidates" remains). 1.3.5. The "all other candidates" option is apportioned equally between the "all other candidate" option for each party and between each independent candidate. 2. Initial tally 2.1. All valid votes are counted and divided by the number of seats to obtain a Hare or Droop quota (the difference is very small in large districts, as you will see). The quota remains the same at each round of voting, ie, incomplete ballots do not result in a reduction of the quota. This is to avoid candidates being elected with different numbers of votes. In standard STV this would result in some unfilled seats. With this method this should also happen, but to a lesser degree. 2.2. First preferences are examined. Only individual preferences are considered. 2.2.1. Non-tied individual preferences are counted. Candidates who reach quota are elected. Their surpluses go (in proportion to the excess, as in fractional STV) to their second preferences, which may be either individual or collective. 2.2.2. Tied individual preferences (including the "individual" fractions of "mixed" preferences) are counted next. For each vote, they are distributed equally between the tied unelected candidates. Candidates who reach quota at this stage are elected as well, but their surpluses are distributed immediately and equally between the remaining candidates of the tie. Candidates who reach quota in this way are elected as well and their surpluses distributed equally between the remaining candidates of the tie. This goes on until no candidate reaches quota. 2.2.3. Steps 2.2.1 and 2.2.2 are repeated with the following individual and mixed preferences. For each vote, the cycle stops when a collective preference is reached. This round of counting finally stops when no further candidates reach quota. 2.3. Collective preferences (including the "collective" fractions of "mixed" preferences) are examined next. In each round of counting: 2.3.1. Ties between collective preferences (ie, between different parties) are apportioned equally between the parties. 2.3.2. Within each party, each vote or fraction thereof goes to the unelected candidate who (a) is not ranked lower as an individual and (b) had most votes from step 2.2. 2.3.3. If the candidate from step 2.3.2 reaches quota, she is elected and her surplus goes to the next most voted unelected candidate of the party (or the succeeding one if the vote ranked him lower as an individual), and so on until nobody else is elected for that party. 2.3.4. The same is done for all parties. 3. Elimination of least-voted candidates 3.1. The candidate with least votes is eliminated. If in a vote he is part of a tie, the surplus is distributed equally between all the other unelected candidates and parties tied. If in a vote he is not part of a tie, the surplus goes to the next preference. 3.2. Step 2 is repeated all over again (but this time should be much shorter). 3.3. Steps 3.1. and 3.2 are repeated until no unelected candidates remain. No candidate is ever elected, on any round, unless he reaches quota. ____________________________________________________________________________ __________________________ I also want to call your attention to the following possibility of strategic voting in fractional STV (including the version above): If my first preference is a very popular candidate, bound to win, I do not vote for her. She will get elected anyway, but my vote will not lose value when it is transferred to my next preference. Regards, Alejandro Solá. <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META content="text/html; charset=iso-8859-1" http-equiv=Content-Type> <META content="MSHTML 5.00.3013.2600" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY bgColor=#ffffff> <DIV align=justify><FONT face=Arial size=2>I suggest the following system for multi-member elections. Please relay to the Elections Methods List and other interested parties.</FONT></DIV> <DIV align=justify> </DIV> <DIV align=justify> </DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2><STRONG>1. Ballot paper</STRONG></FONT></DIV> <DIV align=justify> </DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2>1.1. Whether on paper or on screen, the "ballot paper" lists the candidates in columns, one for each political party. Independents are listed on a separate column. Voters enter the number of their preference besides each candidate's name. I choose to call these "individual preferences" (ie, preferences for individual candidates). Up to now, exactly the same as in STV.</FONT></DIV> <DIV align=justify> </DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2>1.2. But at the bottom of each party's column, there is a slot for "all other candidates for this party". And at the very bottom of the ballot, there is a slot for "all other candidates". I choose to call these "collective preferences". The advantages of collective preferences, especially on very long ballots (such as those necessary in a single national constituency, which I advocate), are twofold:</FONT></DIV> <DIV align=justify><FONT face=Arial size=2>a) allows party voting for those voters who don't know candidates well enough;</FONT></DIV> <DIV align=justify><FONT face=Arial size=2>b) allows easy ranking of most disliked as well as most liked candidates. Simply mark your first preferences for the candidates you like most, then rank "all other candidates", and lastly rank those you like least.</FONT></DIV> <DIV align=justify> </DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2>1.3. Apart from the ties implied by collective preferences, candidates can indicate ties by ranking equally several preferences (individual and/or collective). Each tied entry is given an equal fraction of the vote.</FONT></DIV> <BLOCKQUOTE style="MARGIN-RIGHT: 0px"> <DIV align=justify><FONT face=Arial size=2>1.3.1. Ties consisting exclusively of individual preferences are considered individual preferences.</FONT></DIV> <DIV align=justify><FONT face=Arial size=2></FONT> </DIV> <DIV align=justify><FONT face=Arial size=2>1.3.2. Ties consisting wholly of individual preferences are considered collective preferences.</FONT></DIV> <DIV align=justify><FONT face=Arial size=2></FONT> </DIV> <DIV align=justify><FONT face=Arial size=2>1.3.3. Ties including both individual and collective preferences are apportioned between individual and collective preferences. In these preferences, each individual and collective mark account for an equal fraction of the vote (ie, if it so appears, my entry for William Hague weighs the same as my same-ranked preference for "all other Labour Party candidates").</FONT></DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2>1.3.4. Any individual preference tied with a collective preference including it (ie, the voter ranked equally Tony Blair and "all other Labour Party candidates") is "submerged" within the collective preference (ie, only the ranking for "all other Labour Party candidates" remains).</FONT></DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2>1.3.5. The "all other candidates" option is apportioned equally between the "all other candidate" option for each party and between each independent candidate.</FONT></DIV></BLOCKQUOTE> <DIV align=justify> </DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2><STRONG>2. Initial tally</STRONG></FONT></DIV> <DIV align=justify> </DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2>2.1. All valid votes are counted and divided by the number of seats to obtain a Hare or Droop quota (the difference is very small in large districts, as you will see). The quota remains the same at each round of voting, ie, incomplete ballots do not result in a reduction of the quota. This is to avoid candidates being elected with different numbers of votes. In standard STV this would result in some unfilled seats. With this method this should also happen, but to a lesser degree.</FONT></DIV> <DIV align=justify> </DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2>2.2. First preferences are examined. Only individual preferences are considered.</FONT></DIV> <BLOCKQUOTE style="MARGIN-RIGHT: 0px"> <DIV align=justify><FONT face=Arial size=2>2.2.1. Non-tied individual preferences are counted. Candidates who reach quota are elected. Their surpluses go (in proportion to the excess, as in fractional STV) to their second preferences, which may be either individual or collective.</FONT></DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2>2.2.2. Tied individual preferences (including the "individual" fractions of "mixed" preferences) are counted next. For each vote, they are distributed equally between the tied unelected candidates. Candidates who reach quota at this stage are elected as well, but their surpluses are distributed immediately and equally between the remaining candidates of the tie. Candidates who reach quota in this way are elected as well and their surpluses distributed equally between the remaining candidates of the tie. This goes on until no candidate reaches quota.</FONT></DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2>2.2.3. Steps 2.2.1 and 2.2.2 are repeated with the following individual and mixed preferences. For each vote, the cycle stops when a collective preference is reached. This round of counting finally stops when no further candidates reach quota.</FONT></DIV></BLOCKQUOTE> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2>2.3. Collective preferences (including the "collective" fractions of "mixed" preferences) are examined next. In each round of counting:</FONT></DIV> <BLOCKQUOTE style="MARGIN-RIGHT: 0px"> <DIV align=justify><FONT face=Arial size=2>2.3.1. Ties between collective preferences (ie, between different parties) are apportioned equally between the parties.</FONT></DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2>2.3.2. Within each party, each vote or fraction thereof goes to the unelected candidate who (a) is not ranked lower as an individual and (b) had most votes from step 2.2.</FONT></DIV> <DIV align=justify><FONT face=Arial size=2></FONT> </DIV> <DIV align=justify><FONT face=Arial size=2>2.3.3. If the candidate from step 2.3.2 reaches quota, she is elected and her surplus goes to the next most voted unelected candidate of the party (or the succeeding one if the vote ranked him lower as an individual), and so on until nobody else is elected for that party.</FONT></DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2>2.3.4. The same is done for all parties.</FONT></DIV></BLOCKQUOTE> <DIV align=justify> </DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2><STRONG>3. Elimination of least-voted candidates</STRONG></FONT></DIV> <DIV align=justify> </DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2>3.1. The candidate with least votes is eliminated. If in a vote he is part of a tie, the surplus is distributed equally between all the other unelected candidates and parties tied. If in a vote he is not part of a tie, the surplus goes to the next preference.</FONT></DIV> <DIV align=justify> </DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2>3.2. Step 2 is repeated all over again (but this time should be much shorter).</FONT></DIV> <DIV align=justify> </DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2>3.3. Steps 3.1. and 3.2 are repeated until no unelected candidates remain. No candidate is ever elected, on any round, unless he reaches quota.</FONT></DIV> <DIV align=justify> </DIV> <DIV align=justify> </DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2>_____________________________________________________________________ _________________________________</FONT></DIV> <DIV align=justify> </DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2>I also want to call your attention to the following possibility of strategic voting in fractional STV (including the version above):</FONT></DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2>If my first preference is a very popular candidate, bound to win, I do not vote for her. She will get elected anyway, but my vote will not lose value when it is transferred to my next preference.</FONT></DIV> <DIV align=justify> </DIV> <DIV align=justify> </DIV> <DIV align=justify> </DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2>Regards,</FONT></DIV> <DIV align=justify> </DIV> <DIV align=justify> </DIV> <DIV align=justify><FONT face=Arial size=2><EM>Alejandro Solá.</EM></FONT></DIV></BODY></HTML>
