Re: [EM] STV when applied to choosing pizza toppings
From: [EMAIL PROTECTED] Does anyone have any comments in reference to this critique of STV as applied to choosing three pizza toppings? The issue is whether it's fair to transfer the surplus votes from the winners before transfering votes from the losers. In PR-STV, the number of wasted votes is reduced to 1/(Seats+1). In your example, there are 156 votes. This means that the number of wasted/disenfranchised voters is at most 156/3 = 52 The cost to "buy" a seat is always one Droop quota so it is fair to everyone. The fact that it eliminates candidates last is actually a good thing for them as it allows candidates receive transfers so they can reach the quota. Those 56 NAP members who didn't vote pepperoni first may ALL have voted (yuk) anchovies as their second choice But by not doing that the mushroom and onion voters got their first choice. I am not sure it is fair to call them disenfranchised. The fact that STV doesn't look at later choices is considered a feature called "later no harm". This means that ranking later candidates can never hurt your higher choices. This allows voters give their full list without fear that they will hurt their first choice. Raphfrk Interesting site "what if anyone could modify the laws" www.wikocracy.com Check Out the new free AIM(R) Mail -- 2 GB of storage and industry-leading spam and email virus protection. election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] STV when applied to choosing pizza toppings
Nathan Larson asked: Does anyone have any comments in reference to this critique of STV as applied to choosing three pizza toppings? The issue is whether it's fair to transfer the surplus votes from the winners before transferring votes from the losers. The person who wrote the comments you quoted (below) does not understand the origins of STV-PR or understand how it is generally intended to work. Instead, the writer shows a classical social choice approach to interpreting the information on the ballot papers. But the preferences marked on an STV-PR ballot paper should not be interpreted in that way. Instead, they should be seen for what they are, contingency choices, to be brought into play ONLY in the event that the voter cannot be represented by his or her first choice candidate. STV-PR was not devised in an attempt to identify some great community-wide consensus (maximising some imputed social utility). Rather, STV-PR was devised to ensure that each significant point of view within the electorate was represented fairly (as expressed by the voters' responses to the candidates who had offered themselves for election). Originally, the intent was to maximise the diversity of representation rather than maximise the consensus of representation, but there has been some de facto shift in that by changes made to the counting rules (for the extremes, compare Dáil Éireann STV rules with Meek STV rules).. One of the undertakings normally given to voters in any STV-PR election is: under no circumstances can a later preference harm an earlier preference. This is completely consistency with the 'contingency choice' approach to marking preferences. Any other approach would discourage voters from marking all the preferences they really have or, worse, open the door to tactical voting on a large scale. Seen from this perspective, it will be clear that it is essential to transfer any surplus before you consider the exclusion of the candidate(s) with fewest votes. Where the surplus is so small that it could not change the order of the bottom candidates, some STV counting rules provide for the transfer to be held in abeyance, but that doesn't alter the general principle. James Gilmour --- What you describe would indeed work, however Suppose the second choices of the 100 winner (pepperoni) votes were one half for mushrooms, one half for onions. This, if I follow the numbers correctly, means that mushrooms and onions would win (with 40 and 56 respectively). But look: you have completely ignored the second (and third) choices of the folks who didn't vote for pepperoni as first place. You just disenfranchised 56 voters. Why should only the pepperoni-first voters be the ones who get to exercise their second and (possibly) third choices? Doesn't seem fair to me! Those 56 NAP members who didn't vote pepperoni first may ALL have voted (yuk) anchovies as their second choice. Clearly that would exceed the quota and anchovies would have garnered MORE votes that any of the non-pepperoni choices. But you trashed them. For shame! With smaller numbers the problems become more apparent. I am taking the liberty of e-mailing you directly the essay I did some years ago. Enjoy! Meanwhile I'll think about constructing a counter example where there is no choice but an arbitrary choice (following your rules) that causes a different outcome. But not tonight. Too late. John John D. Stackpole, CPP, PRP Voice: 301.292.9479 Parliamentary Services Fax: 301.292.9527 11 Battersea Ln. [EMAIL PROTECTED] Ft. Washington, MD 20744-7203 election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] STV when applied to choosing pizza toppings
Jonathan Lundell Sent: 13 November 2006 16:27 At 11:37 AM + 11/13/06, James Gilmour wrote: Rather, STV-PR was devised to ensure that each significant point of view within the electorate was represented fairly (as expressed by the voters' responses to the candidates who had offered themselves for election). Originally, the intent was to maximise the diversity of representation rather than maximise the consensus of representation, but there has been some de facto shift in that by changes made to the counting rules (for the extremes, compare Dáil Éireann STV rules with Meek STV rules).. Would you elaborate, please, on what you mean by diversity vs. consensus of representation, and how Meek maximizes the latter over the former? Or point me to something I should be reading? This analysis of 'diversity vs. consensus' has not been written up anywhere, but it is on my to do list, as an article for 'Voting matters'. Meantime I have copied the text from a post last March to another list in which I was concentrating on how consequential surpluses are transferred, and have added a bit at the end. There are currently five different methods (of transferring consequential surpluses) for use in STV-PR elections (leaving aside the Cambridge, MA, rules which have their own peculiarities). In the Dáil Éireann rules the surplus votes are carried as integer votes on the appropriate number of ballot papers (each ballot paper of value 1 vote). These ballot papers are selected only from the last parcel received by the newly elected candidate, i.e. from the parcel that created the surplus. To minimise chance effects, the last parcel is sorted into sub-parcels according the next available preferences (candidates not yet elected) and a due proportion of ballot papers is then taken from each sub-parcel. This process inevitably involves an element of chance that may or may not affect the outcome of the election. To eliminate the element of chance, ballot papers can be transferred at fractional values, as suggested by Gregory in Australia in 1880; hence this is known as the Gregory Method (GM). All the papers in the last parcel received are sorted according to next available preferences. Any that are non-transferable are set aside and the votes carried on those papers are retained as part of the newly elected candidate's quota. If the total value of the transferable papers does not exceed the surplus, the papers are transferred at their current value. If the total value of the transferable papers exceeds the surplus, the value of each paper (all of one value) is reduced: the new transfer value of each ballot paper equals the surplus divided by the number of transferable papers. Some consider that taking only the last parcel received as inherently unfair or defective or just a shortcut for manual counting and so have devised methods to transfer ALL of a candidates ballot papers when that candidate is elected with a surplus. These are the inclusive methods of handling consequential surpluses. The Inclusive Gregory Method (IGM) is used in the STV-PR elections to the Australian Federal Senate and to some Australian State legislatures. In this method, all of the ballot papers of a newly elected candidate are sorted according to the next available preference and an AVERAGE transfer value is calculated by dividing the surplus by the total number of ballot papers then held by the newly elected candidate. Non-transferable papers are set aside as non-transferable, taking with them the proportionate share of the surplus. This method (IGM) is fundamentally flawed and should never be used because the process of calculating an average transfer value for all ballot papers has the effect of INCREASING the total contribution of some ballot papers to more than 1 vote, and correspondingly decreasing the contribution of some other ballot papers to less than 1 vote. This violates the principle of one person, one vote and should have been declared unconstitutional. The Weighted Inclusive Gregory Method (WIGM) overcomes the defect in IGM described immediate above. In this method, all of the ballot papers of the newly elected candidate are sorted according to the next available preference. A 'surplus fraction' is first calculated: the 'surplus fraction' equals the surplus divided by the candidate's total present vote. Then the 'continuing transfer value' of each paper is calculated: equals the current value of the ballot paper multiplied by the surplus fraction. Non-transferable papers are set aside as non-transferable, taking with them the proportionate share of the surplus. This method ensures that each ballot paper contributes in total 1 vote to the election. WIGM has not yet been implemented for public elections anywhere in the world. It was proposed for STV-PR elections to the Western Australia Legislature, but the Electoral Reform Bill was withdrawn (for reasons not related at all to WIGM) - since
[EM] STV when applied to choosing pizza toppings
Does anyone have any comments in reference to this critique of STV as applied to choosing three pizza toppings? The issue is whether it's fair to transfer the surplus votes from the winners before transfering votes from the losers. ---What you describe would indeed work, however Suppose the second choices of the 100 winner (pepperoni) votes were one half for mushrooms, one half for onions. This, if I follow the numbers correctly, means that mushrooms and onions would win (with 40 and 56 respectively). But look: you have completely ignored the second (and third) choices of the folks who didn't vote for pepperoni as first place. You just disenfranchised 56 voters. Why should only the pepperoni-first voters be the ones who get to exercise their second and (possibly) third choices? Doesn't seem fair to me! Those 56 NAP members who didn't vote pepperoni first may ALL have voted (yuk) anchovies as their second choice. Clearly that would exceed the quota and anchovies would have garnered MORE votes that any of the non-pepperoni choices. But you trashed them. For shame! With smaller numbers the problems become more apparent. I am taking the liberty of e-mailing you directly the essay I did some years ago. Enjoy! Meanwhile I'll think about constructing a counter example where there is no choice but an arbitrary choice (following your rules) that causes a different outcome. But not tonight. Too late. John John D. Stackpole, CPP, PRP Voice: 301.292.9479 Parliamentary Services Fax: 301.292.9527 11 Battersea Ln. [EMAIL PROTECTED] Ft. Washington, MD 20744-7203 Nathan Larson wrote: Here is an example to illustrate how surplus votes would be transfered proportionately under STV. Suppose a state's NAP convention wants to order an extremely large pizza, but the coupon only allows three toppings. In accordance with the bylaws, everyone submits their preferential ballots and the tabulation is conducted using STV. The first choices are as follows: Pepperoni: 100 votes Onions: 26 votes Green peppers: 20 votes Mushrooms: 10 votes Anchovies: 0 votes The Droop quota is [Votes / (Toppings + 1) + 1], which simplifies to [156 / (3 + 1)] + 1, or 40. Pepperoni, with 100 votes, meets the 40-vote quota, so it is declared elected, and there are 60 surplus votes. Suppose that for the 100 voters who picked pepperoni as their first choice, their second choices were as follows: Mushrooms: 50 second-choice votes Onions: 25 second-choice votes Anchovies: 25 second-choice votes The 60 surplus votes for pepperoni would be distributed proportionately, as follows: Mushrooms: +30 votes (50% of 60) Onions: +15 votes (25% of 60) Anchovies: +15 votes (25% of 60) The standings would then be as follows: Pepperoni: 40 votes (elected) Onions: 26 + 15 = 41 votes (elected) Green peppers: 20 votes Mushrooms: 10 + 30 = 40 votes (elected) Anchovies: 0 + 15 = 15 votes The decision, then, would be to buy a pizza with pepperoni, onions, and mushrooms. The surplus votes were transfered taking into account the second choices of everyone who chose pepperoni as their first choice. -- Nathan Larson, CPA(H) 540-788-4945(C) 703-298-3838 -- Nathan Larson, CPA(H) 540-788-4945(C) 703-298-3838 election-methods mailing list - see http://electorama.com/em for list info
