7(C|4FF4 3333j4$44$5x5 575*6 z#.c.Basic Parts of CSTV; This voting system introduced here combines rank-order ballots and the Marquis de Condorcet's criterion for selecting a winner, with Thomas Hare's method of eliminating dropping, scratching-out-off candidates until one of the remaining ones meets the selection criterion. Joining Matching these voting rules/ systems produces a descendant one which has all the proven strengths of its parents but and less of their most notable weaknesses. .c2.Rank-order ballots; Rank-order ballots ask a voter to rank the several candidates as first choice, second choice, third and so on for as many candidates as he cares to. True? Must he rank all? Such ballots allow voters to choose among more than two candidates at a time. Voters do not have to deal with complex and highly-manipulable procedural rules this says I want committees to use CSTV about the order in which to vote yes or no on each option, nor tediously-repetitious and manipulable voting in run-off elections, nor long debates to coerce consensus. One ballot quickly and easily compares all of the candidates. The ballots contain enough information to make solid decisions with broad popular support and not likely to be over-turned later. They express most clearly and simply the data needed for finding a candidate who meets Condorcets criterion. Figure 1 shows an example part of a rank-order ballot used for most national elections in Australia and Ireland. Australian and Irish voters use rank-order ballots such as those on the back cover, Voters use rank-order ballots for national elections in Australia and Ireland. Northern Ireland,. Malta, and New York City school board elections It is like a list of the colleges or jobs you want. The one you want is number 1, your second choice is number 2 and so on. Figure I shows an Australian rank-order ballot.  Figure 1. An Irish ballot .c4.Figure 1. An Australian Ballot;  Figure 1. from An Australian Preferential Ballot Melbourne or Sidney newspaper from U of W or Lib of Congress .c2.Condorcets criterion; The Marquis de Condorcet's criterion for picking a winner probably is respected more than any other rule standard. To win, a candidate must be able to be able to beat each of the other candidates in pairwise, one-on-one contests. For this essay I shall call these (potential) Condorcet winners. To decide a pairwise contests without numerous elections we, in effect, electronically sort all of the rank-order ballots into two piles, one for each candidate. If a voter ranked candidate A above candidate B, then that ballot goes in As pile. It does not matter whether the voter put A his favorite one rank or ten ahead of B a rival; either way candidate A the favorite wins that one persons one vote in the comparison of A versus B. When we sort all of the ballots into 2 piles to decide a one-on-one contest, it does not matter whether a voter put his favorite one rank or ten ahead of a rival; either way the favorite wins one vote in that two-candidate comparison. * To the voters we might say If you want your vote to go to candidate A rather than B when we compare A with B, then rank A anywhere somewhere above B. To do that for all pairs of candidates, just list them in the order you like them. [according to your preference. your favorite first down to your ____ last. first choice, second choice . . . to last choice.] The Condorcet rule is not decisive and cannot name any winner if no candidate beats each of the others. We call this a voting paradox or cycle. Candidate A beats B who beats C who beats A. This is shown in Example 1. Recent data from computer simulations and actual elections in the U.S. suggests cycles are very rare. (Table 6 and footnote 19 will show this.) But even a rare occurrence is enough to be a critical major flaw. An indecisive voting rule costs time, confusion, and the legitimacy of the ensuing/ resulting government and laws. To avoid that problem several social scientists have created Condorcet-completion rules. These rules elect the Condorcet winner when one exists and use a variety of secondary rules to resolve a voting cycle when one exists. pick a winner from a voting cycle. CSTV is a Condorcet-completion rule. CSTV is the best such rule. Because of this / To avoid that problem several social scientists have created Condorcet-completion rules which elect the Condorcet winner when one exists, and use a second rule to resolve a voting cycle. / That is why many people have created Condorcet-completion rules for elections. These systems always elect the Condorcet candidate if there is one. But when there is none, each system uses a different method of totaling votes to select a winner. .c5.Example 1. A Voting Cycle; Example 1. A Voting Cycle Interest groups ballotsPairwise comparisonsBallot222 A gets 4 votes to 2 against B etc.ranksvotersvotersvotersABC1st choiceABCA---4:22:42ndBCAB2:4---4:23rdCABC4:22:4--- How to read these tables and diagrams: A bold font marks the winning letter and its pairwise wins. An italic number sometimes marks a pairwise win noted later in the text. The arrows in the diagrams point from the pairwise winner to the loser in each two-candidate contest. Pairwise comparisons A gets 4 votes to 2 for B and so on.ABvoters forvoters forvoters forvoters forROWCOL.ROWCOL.A 4 :2B 2 :4 A Voting Cycle If the voters ballots create a voting cycle, that moves a CSTV election into Hares candidate-elimination process, described next. .c2.Alternative vote; Thomas Hares (1859) single transferable vote is the vote-counting appears to be the decisive rank-order voting rule most likely to induce sincere ballots in large electorates groups. Footnote Chamberlin, Cohen, and Coombs; Merrill [chapter 6]; and Tideman found that Hare (MSTV) offered the fewest opportunities for manipulation of any system tested. Their tests included: single-vote plurality, Black, Borda, Coombs, Dodgson, Kemeny, max-min, and approval voting. (Tables 2, 3, 4, and 5 will show this.) This concerns the frequency of manipulable elections as found in simulations and practise. It does not contradict the theoretical proofs by Gibbard and Satterthwaite that all voting systems are manipulable. [ Check that these were sims of manipulation not just Con or util ef. It eliminates the candidate(s) with the fewest first-place votes, until one candidate meets a selection criterion. * On each voters rank-order ballot, the rank positions gaps left by the eliminated candidate(s) are re-filled as the remaining candidates move up in rank. (That is shown in Example 2b.) Hare required that the winner get a majority of the (recalculated) first-place votes. Eliminations are usually needed to arrive at a majority in contests with more than two candidates. { In contests with more than two candidates, we usually need to eliminate some candidates before one of them can get a majority of the recalculated first-place votes. For this essay I shall call this MSTV for majority single transferable vote. MSTV is used to elect the Australian House of Representatives. (Merrill page 13 or Gudgin and Taylor page 102) * To the voters we might say If you want your vote to go for A as long as she is a candidate, then rank her first. [above the others] If A is dropped (for lack of firsts) who would you want your vote to go to? Rank that candidate second. and so on. Keep that question in mind as you rank all of the candidates. .c5.Example 2. Alternative Vote Eliminates a Candidate; Example 2. Single TransferableVote Eliminates a Candidate a) Original ballots Interest groups ballots Pairwise comparisons Ballot 2 1 2 B gets 3 votes to 2 against A etc. ranks voters voter voters A B C 1st choice A B C A 2:3 3:2 2nd B A B B 3:2 3:2 3rd C C A C 2:3 2:3 A and C each get 2 first-place votes. No one gets the required 3 or more first-place votes needed for a majority of the first-place votes from the 5 voters. So MSTV requires makes an elimination step. Bhas the fewest first-place votes, and so B is eliminated. A and C each move up where needed to fill gaps left by Bs elimination. b) After one elimination step Interest groups ballots Pairwise comparisons Ballot 2 1 2 A wins 3 votes to 2 against C. ranks voters voter voters A C 1st A A C A 3:2 2nd C C A C 2:3 A gets 3 recalculated first-place votes among the remaining candidates and wins. That is a majority so she wins under MSTV. .c1.CSTV; 10 pt line before & 4 pt after this If we combine Condorcets selection criterion with MSTVs Hares elimination criterion we get CSTV. The combined voting system has a Condorcet efficiency of 100%. That means every any time if there is a candidate who meets Condorcets criterion on the initial ballots, she always wins. If no candidate meets that criterion, we eliminate the weakest candidate as defined above. (See the sample worksheets on page 29.) Most importantly, there are few opportunities and great risks for voters or politicians who try to defeat a Condorcet candidate by manipulating an election. possible footnote: Chamberlin 1984 on manipulation is the greatest threat ot the value of voting. Most importantly, there are few opportunities and great risks for manipulations by voters or politicians trying to defeat a candidate who would meet Condorcets criterion. on sincere ballots The next two sections refer to research supporting these assertions. If no candidate meets Condorcets criterion on the initial ballots, then use Hares process of eliminating the candidate(s) with the fewest first-place votes until one of the remaining candidates beats each of the others. .c1.CSTV Compared with MSTV (Hare); .c2.CSTV winners versus MSTV winners; * Is a CSTV winner as strong a candidate as a MSTV winner? Yes. If the two systems pick different winners differ, the CSTV winner is always the stronger because by definition she can beat the MSTV winner in a pairwise contest. Look again at Example 2. Candidate A won under MSTV. But on the original ballots, the CSTV winner, B, beat the MSTV winner by 3 votes to 2 votes. Straffin gives an example in which the Condorcet winner gets a 14 to 3 majority over Hares winner. (Straffin pages 23-25) * When the two systems give elect different winners, CSTVs winner will always beat MSTVs. With these sincere ballots, the Condorcet CSTV winner would loss to the MSTV winner by Borda (4 to 5), but win by Copeland (2 to 0), and Dodgson (0 to -1). Assuming each voter gives approval votes to his 2 favorite candidates, CSTV would also win under approval voting (5 to 3). But if voters give approvals to less than half of the candidates (one in a three-way race) they would create a two-way tie - excluding the CSTV winner. Each of the tied candidates would receive less than 50% approval - hardly a mandate. .c2.Squeeze effect by chance or manipulation; Example 2 can illustrate a Condorcet winner who was squeezed-out of a MSTV election by candidates with very similar appeals slightly to her left and right on the issue(s). These other candidates got more first preferences. While The Condorcet-criterion winner got many second-place votes, but she got few firsts so she was eliminated before either of the two nearby candidates were. Figures 2 and 5 represent this graphically for 1 and 2 issue dimensions respectively. Figure 2 represents this graphically with the number of voters on one dimension and an issue on the other dimension. Figure 5 represents a squeeze on 2 issue dimensions. .c4.Figure 2. A Candidate Squeeze; Figure 2. A Candidate Squeeze Candidates  Opinion positions (along 1 issue dimension) Interest groups Pairwise Comparisons . numbers of voters A loses to B by 6 votes to 10. Ballot I II III IV ranks 6 voters 2 2 6 A B C 1st choice A B B C A 6:10 8:8 2nd B A C B B 10:6 10:6 3rd C C A A C 8:8 6:10 As in Example 2, MSTV would eliminate B , although she can beat both A and C. Candidates A and C then would tie with 8 votes each. and under plurality, runoff. Non-centrist candidates may also get squeezedbut that is not important because it does not change the winner. Is Is This can occur by chance. It can also occur because politicians manipulate an election through by introducing irrelevant alternatives. This sometimes results from a divide-and-conquer strategy in which they secretly help minor candidates on the opposite political wing. These new candidate(s) divide the opposition into several camps, none of which can get enough votes to win. Politicians or voters can do this under MSTV, but less often than under most voting methods.6 CSTV makes the squeeze even harder to do because voters must first create a voting cycle; so CSTV is harder to manipulate. It is even less possible under CSTV because there must first be a voting cycle - which again is rare.5 CSTV makes the squeeze even harder to implement because the insincere coalition must also create a voting cycle. That requires participation through insincere ballots by many more of the coalitions / parties voters. President Nixons Watergate burglars, hired by the Republican Party, tried to hurt the moderate candidates for the Democratic Partys nomination for president. This helped the far-left candidate, McGovern, to win his partys nomination. McGovern was farther from the center of American public opinion than Nixon wasso Nixon won in a landslide. Merrill describes what one politicians must do to create a squeeze under STV voting. Under the Hare [MSTV] system, manipulation on behalf of a candidate normally involves throwing some (but not too much) of the candidates support to a pushover, who may thereby eliminate a chief rival at an early stage. Such a strategy requires a quantitative estimate of the amount of support to be shifted as well as an awkward exhortation to supporters to give first preference to another candidate in order to help their favorite. This strategy, if it is possible at all, is at once difficult to design and implausible to implement in a large electorate. (Merrill, page 75) (See also tables 2 and 3.) To the best of my knowledge, no one has ever implemented this strategy. Several other factors make manipulations of MSTV hard. 1)Transferable-vote strategists usually must start with many more first-place voters than the candidate they want to squeeze-out. at least enough to give some away. The squeeze often requires the manipulators have more firsts than any other candidate. 2)Strategists often must know all other voters complete preference orders if they want to know which candidate to eliminate so formerly low-ranking votes become firsts for the their nominee, or at least dont transfer to a major rival. { Complete preferences are much harder to guess than who the major candidates or voters first preferences are. It is not enough to know only who the names of the leading candidates or voters first preferences. are Also, 3)The number of supporters who must be encouraged to change their first preferences covers a narrow range. In this sense the window of opportunity does not open [often or ]wide. when it is open at all, is very small. If strategists guess other voters preferences incorrectly or if too many conspirators give away their first preferences, then they decrease their chance of winning. 4)High risks of helping to elect someone even less desirable than the candidate who would win on sincere voting to you than the Condorcet candidate also inhibit abuses of the single transferable vote: one usually must squeeze-out the Condorcet-criterion winner carefully, without electing the opposite jaw of the vice. All this makes CSTV and MSTV strategies riskier than those for any other voting systems. The risks under CSTV are higher than under MSTV or any other rank-order or utility system yet tested. To the voters we might suggest Dont reveal your preference list. Argue strongly for your favorite and against your major rival. Argue for or against the other candidates but dont let anyone know what order you rank the jokers in. bums the middle .c2.Manipulation of both CSTV and MSTV; It is possible to manipulate any voting system, sometimes, including CSTV. But it is rarely possible, rather difficult and very risky. To manipulate CSTV, one must have a voting cycle. footnote Chamberlins 1986 article. If a voting cycle would occur without manipulation then one only needs to put the sincere-STV winner in a squeeze. But natural voting cycles are rare (Table 1) and in a squeeze is both rarely possible (Table 6) and even then difficult to achieve. If a cycle does not occur naturally and if the STV rule does not elect the the Condorcet winner, then supporters of the STVs winner can manipulate the election by raising an unknown above the Condorcet winner to create a voting cycle. (The unknown then beats the former Condorcet winner who still beats the STV winner who still beats the unknown.) Condorcets rule can find no clear winner so the election is decided by the STV rule., eliminating candidates until one of those remaining wins by Condorcets rule. Creating a voting cycle often requires a large conspricy of voters, but it is always mathematically possible and voters can follow the strategy easily. If the manipulation succeeds it makes CSTV elect the same candidate MSTV would without manipulation. So CSTV does no worse than MSTV although more manipulable. We will estimate the opportunities for this manipulation in the next section. If Condorcet and STV pick the same winners, then strategists must create a voting cycle and also, on the same vote, squeeze-out the former Condorcet winner. This is the most common election pattern and the hardest to manipulate. In fact it is as often impossible to manipulate as STV is (Table 6). See page G. non-mon: Draw a bell curve x___A__B___C__ with B at the center. A is closer to the center than C is. As supporters vote for C over B to create a cycle. They hope to then squeeze out B. MSTV does not have this problem. But if there is a voting cycle then there is no majority - until eliminations create one. .c5.Example 3. A Cycle and Squeeze; 16 voters: 7 (1, 4, 2), 2, 3, 4. If 2 too many of As supporters change their first preferences, they elect C, their least favorite candidate. 21 voters: 10 (2, 4, 2), 3, 3, 5. If 1 too many of As supporters change their first preferences, they elect C, their least favorite candidate. Example 3. A Cycle and Squeeze a) sincere ballots Interest GroupsBallotIIIIIIIVranks10 voters3 voters3 voters5 voters1st choiceABBC2ndBACB3rdCCAA Pairwise comparisons .ABCA10 : 1113 : 8B11 : 1016 : 5C8 : 135: 16 B beats both A and C, so CSTV would elect B is a Condorcet winner. b) with strategic voting by As party Interest GroupsBallotIiIiiIiiiIIIIIIVranks2 voters4 voters4 voters3 voters3 voters5 voters1st choiceCAABBC2ndACBACB3rdBBCCAA Pairwise comparisons .ABCA10 : 1111 : 10B11:1010 : 11C10:1111:10 B beats A who beats C who now beats B. The 6 voters who moved C above B have created a voting cycle. No one wins by Condorcets criterion so CSTV requires an elimination. Now that 2 of As supporters have given their first preferences to C, C has more first-place votes than B. So we eliminate B. c) after one elimination Interest GroupsBallotIiIiiIiiiIIIIIIVranks2 voters4 voters4 voters3 voters3 voters5 voters1st choiceCAAACC2ndACCCAA Pairwise comparisons .ACA11 : 10C10:11 A wins. Some political scientists argue that polarized societies benefit from decisive action more than from compromise. I tend to disagree. That is the worst of majority tyranny. In any case, The opportunities for this rarely occur and contain great risks. If too many of As supporters, one more in this example, change their first preferences, they elect C, their least favorite candidate. For the Hare system, there exists a much smaller target that manipulators must hit if they are to be successful. Only the 2 insincere voters in group Ii were needed to create the first-preference squeeze for MSTV. But the cycle required to manipulate CSTV needed 6 insincere voters: those 2 plus the 4 voters under Iii. Three times more conspirators were needed to manipulate CSTV than MSTV. This will be common. By this measure CSTV elections are harder to manipulate away from a Condorcet winner than MSTV elections are. fails to elect the Condorcet winner are a subset of those in which MSTV does because the Condorcet rule is not subject to squeezes nor irrelevant alternatives, and because it requires larger conspriacies needed to create voting cycles.> Voters under I i and I ii help C beat B to create a voting cycle. The 2 voters in I i risk eliminating A in order to eliminate B . Voters in I i and I ii create a voting cycle, provided that A still beats C. A large party can often, prehaps always, create a voting cycle by adding their votes to those of a minor party and so help the smaller partys candidate beat the leader. They can do this with little risk of the minor candidate beating their favorite candidate if other groups dont shift to support that minor candidate and thus make her the Condorcet winner. .c2.Non-monotonicity by chance or manipulation; Occasionally, in some voting systems, a voter can hurt a candidate by raising her rank toward number one the top. The candidate might win on a pre-election poll, but then lose the election after some voters jump on her the bandwagon and move her up to first choice. We call this system-level behavior non-monotonic. We say that systems which sometimes behave this way are not monotonic. / This pattern is called non-monotonicity. Non-monotonicity is like a bad volume control on a stereo amplifier. You turn the nob up and usually the volume goes up. But sometimes a bit of corrosion inside makes the volume drop lower than it was before you turned the nob. Hey! Whats going on here? Or think of it as Or it is like a bad faucet: you turn the hot-water nob down and suddenly get scorched!  Ouch! Hares elimination process has another fault called non-monotonicity. With this ...a candidate can achieve a win because of a loss of support (or fail to win because of a gain in support).(Merrill, page 10,75) Monotonicity criterion: If x is a winner under a voting rule, and one or more voters change their preferences in a way favorable to x (without changing any other alternatives), then x should still be a winner.(Straffin:24) Is is Simply in terms of logic thats a serious flaw for a decision rule. It is a theoretical possibility with any elimination process including Hares. Voters in a non-monotonic voting system might help a candidate by lowering her rank as two of As supporters deliberately did helped her in Example 3. (Four other voters deliberately dropped the leading candidate, B, to hurt her but that was monotonic.) Or they might intentionally or unintentionally hurt a candidate by raising her rank. In the next example, the two voters on the right will raise the leading candidate and cause her to lose . .c5.Example 4. Non-monotonicity in CSTV and MSTV; Example 4. Non-monotonicity in CSTV and MSTV From Straffin, page 22 BallotInterest groups.ranks6 voters5 voters4 voters2 voters1st choiceACBB2ndBACA3rdCBAC Pairwise comparisons .ABCA11:68:9B6:1112:5C9:85:12 A beats B, who beats C, who beats A. No one wins a majority over all nor over each of the others. Both MSTV and CSTV require elimination of the candidate with the fewest first-place votes: C. Then A wins, 11 votes to 6 votes against B. Suppose the two voters on the right decided to rank A above B. B would then have fewer firsts than C. We would eliminate B. C would beat A by 9 votes to 8. Imagine the news report: C won the election, but if A had received fewer first place votes, she would have won. In a recent article about this phenomenon, Dorn and Kronick imagine a news announcement: Candidate C won today, but if A had received fewer first place votes, she would have won. (Straffin page 24) Notice that an elimination is necessary to give a non-monotonic result. Suppose A can win by MSTV without eliminations on the first poll, getting a small majority over all the other candidates combined or by Condorcet. If she gets more support later, [then she ]will win by a larger majority. But if As victory depends on facing B not C, then a shift of support from B to A may derail undermine As that weak victory. This offers another potential route for manipulating a MSTV or CSTV election. But most Australian political observers seem to discount the frequency of this pattern this phenomenon after more than 70 years of experience with Hares elimination process. Quote or at least cite them. The opportunities for it are even rarer than those for the squeeze play. The improbability of both is reflected in the difficulty of manipulating Hare as reported by Chamberlin (1984), and Tideman and will be shown in the next section. Table 2. and footnote 7. xc3 Non-monotonicity of CSTV versus MSTV This problem will occur even less with CSTV than with MSTV. CSTV winners need to meet only the Condorcet criterion, not the majority criterion required by Hare. We do not have to eliminate candidates until one gets a majority of the first-place votes we usually find a Condorcet winner before that. For almost all elections we would not have to eliminate anyone. (See footnote 5 and Table 1.) The CSTV elections which require eliminations are a subset of the MSTV elections which do so. Hence we have CSTV has much less chance of causing a non-monotonicity through the eliminations. .c6.Table 1. Frequencies of Majority and Condorcet Winners; Table 1. Frequencies of Majority and Condorcet Winners in computer-simulated elections with 4 candidates could go in footnote data only? from Chamberlin and Cohen (1978) Electorate sizes 21 voters 1000 voters Majority Condorcet Majority Condorcet Impartial Culture .03 .84 .00 .85 Low Candidate Dispersion .30 .92 .00 .99 Medium Dispersion .10 .98 .10 1.00 High Candidate Dispersion .40 .98 .30 1.00 The last example will contrast what can happen when we have a Condorcet CSTV winner but no majority MSTV winner. format tables .c5.Example 5. Non-monotonicity for MSTV but not for CSTV; Example 5. Non-monotonicity for MSTV but not for CSTV Interest groups ballots Pairwise comparisons .Ballot566A beats B, 11 votes to 6. .ranksvotersvotersvotersABC1st choiceABCA11:611:62ndBAAB6:1111:63rdCCBC6:116:11A beats both B and C. A is the Condorcet and CSTV winner. But no one gets a majority so MSTV requires elimination of the candidate with the fewest firsts, A. b) After the elimination of A Interest groups ballots Pairwise comparisons .Ballot566ranksvotersvotersvotersBC1stBBCB11:62ndCCBC6:11With the help of As party B beats C by 11 to 6. So B is MSTVs winner.So MSTV would elect B. But suppose 2 of Cs supporters decide they like B best and so change their first choice from C to B. c) After 2 voters shift from C to B Interest groups ballots Pairwise comparisons .Ballot5642ranksvotersvotersvotersvotersABC1stABCBA9:811:62ndBAACB8:913:43rdCCBAC6:114:13A is still the Condorcet winner. But now MSTV will eliminate C instead of A. d) After the elimination of C Interest groups ballots Pairwise comparisons .Ballot5642ranksvotersvotersvotersvotersAB1stABABA9:82ndBABAB8:9A defeats B by 9 to 8 (or 11 to 6 if the 2 voters keep A in second place and drop C from first to last). So MSTVs winner in the first poll was defeated due to because of a gain in support. Notice that As party could not produce this victory by changing their own ballots. So defeating the leading candidate by raising her rank is not a likely means of manipulation even in MSTV. [ It simply occurs as a random flaw in the elimination process. It is probably only a rare possibility given the patterns of preferences in actual electorates. This example and Table 1 strongly suggest that it happens even more rarely for CSTV than for MSTV. ] This is not a proof because there might be counter-examples. * To sum-up this section on CSTV versus MSTV: CSTV is often harder to manipulate, more often monotone, and when the two systems pick different winners, CSTVs winners always beat MSTVs. Possible manipulations are at least as rare and risky. Manipulations are harder to organize. CSTV is more often monotonic. When the two systems pick different winners, CSTVs winners always beat MSTVs.  Candidates under CSTV can be answers to survey questions, or initiatives, resolutions and bills, with and without amendments, or candidates for solitary positions such as judges, attorneys general, treasurers, and chief executives. Move this to Uses/Recommendations. None or the status quo should be a candidate in any election. None should be given the top position on the ballot list. That is because voters tend to favor the top positions, particularly the first. This favor should not go to any one of the major candidates. Multi-candidate ballots give less advantage to the top position than two-candidate ballots do. [the average amount of advantage]  For clarity, I shall use masculine pronouns for voters and feminine pronouns for candidates to help us distinguish these actors. ..to help distinguish among these actors. solely for clarity I want to write about human actors rather than pure abstractions such as the insincere ballot.  Some agenda setting is necessary even with multi-candidate voting systems. For example, take a large piece of legislation with several policy areas to be decided and several options for each policy. This leads to an array of choices a decision matrix such as 4 x 3 x 5...= a very large number. But most of us simply cannot study, comprehend, and rank more than 5 to 10 such alternatives at a time. So we must break-up the array into policy areas: 4 options, then 3, then 5 and so on. Multi-candidate voting systems then may let us pick each policy areas option without agenda rigging. / effects But whoever decides which policy area comes first and which one last might effect their outcomes but less easily and with fewer opportunities for manipulation of the agenda than we see now. Move this to Purpose of Gov. area = dept / agency / Some agenda setting is necessary in multi-candidate voting systems. Take, for example a large budget with several departments and several options for each department. This leads to an array of choices such as 4 x 3 x 5...= a very large number. But most people can not study, comprehend, and rank more than 5 to 10 such alternatives at a time. So we must break-up the array by departments: 4 choices, then 3, then 5 and so on. Multi-candidate voting systems may let us decide each departments budget without agenda rigging. But in the case of funding, whoever decides which department comes first and which department last can effect their relative funding. The defects of the most often-used voting system, plurality, are widely felt, if not always completely understood. Chamberlin, Straffin, and Merrill each show plurality to be the worst voting system by their measures. Move, but to where in body? intro?  Born in 1743, Condorcet became an eminent mathematician, elected secretary of the Academy of Sciences and a member of the French Academy. During the French Revolution he was elected to represent Paris in the Legislative Assembly and became its secretary. He was chief author of the Address to the European Powers, the scheme for a system of state supported education, the declaration calling for suspension of the King and summoning the National Convention to which he offered a constitution representative of the moderate Girondins. The radical Jacobins defeated that constitution and eventually outlawed Condorcet for his forthright advocacy of political moderation. He died in prison in 1794.  No criterion for evaluating voting systems appears more persuasive than that by the Marquis de Condorcet. (Merrill, page 15) All variants of democratic theory endow a Condorcet winner with a certain degree of legitimacy, and such a mandate is no doubt a vital ingredient in the subsequent career of the winner. (Chamberlin, Cohen, and Coombs, 1984) Check and add more quotes from Merrill, none math books.. Biog note on Condorcet.  I do not propose renaming single-winner Hare as MSTV. Likewise CSTV is only a temporary reminder of the new systems parts. Any descriptive name is apt to be misleading so we should maintain the tradition of using inventors surnames to label voting systems.  Readers can get a better feel for CSTV by ordering, say, pizza using the blank ballots and worksheets on page 26.  Note that there cannot be different CSTV and MSTV winners in the same elimination step round. Any MSTV winner, having an absolute majority over all other candidates combined, must also have a majority over each of the other candidates and therefore also wins by CSTV.  Non-monotonic comes Latin words which mean not in harmony, not in unison, or not moving together.  An impartial culture has voters distributed evenly (randomly) across the range of opinions on an issue.  This spatial-model culture has more voters in the center than on either side. A low candidate dispersion means the average candidate takes a stand closer to the center of position on an issue than the average voter. This corresponds to the assumption that most candidates try to please the large group of moderate voters in the center.  Loring Condorcet, single transferable vote  v_re ajRY\RYLQX   +A  DW+CB  B!P2(L"C QXq    " q0,>7>,002347>,"B"%  ;G (D4  +((2   ( 4  8 E)%2  I+W+4  ;9G?(D:2nn :~ ,~ } }"g/ ""t6 sKrIg/UK?$ ssKsJ "rI##############g##{###  }Є "rI#######g#{#"cB t&"ts$cBK^Dgtt" "s$#### ##/##^###  }Є "s$## #/#^#"t t"ttt t "t########m#  }Є #####m" """"t&ttttt "t## ####l#####  }Є ## ##l##"x #  (? # of voters _E E _ 0HHHHHHP``    } sXs  F|U +I  FU)%II   FU)III   FU)%IV  "z0 (,{A  #1+BB  Zh(dC }"& t&.*&*.* "*#######  }Є "*"HtHVVHJLV "V###### #  }Є "1"1%  S_ (\8  7xC(@y8  $(!6  $)10  7C+10  S_(\6 }"l; "sL######################## }"rK######################################################################################### Q"2 X  $0(.C } Q X  ( B }"n0 "t# ###### }"s"################################# Q!v1 X  #x/(-yARYRYuQX   +A  DW+CB  B!P2(L"C QXq    " q0,?7?,002347?,"Bq0?#?#420 ?#"  ;G (D8  +((13   %( 10  5 G)11  I+W+16  ;9G?(D:5RYRYwQX   +A  DW+BB  B!P2(L"C QXq    " q8(BB(>&;$8B"&;q0?$?$420 ?$"  : F (C10  + ((11   $( 10  6 C)!11  H+V+10  ::FH(C;11?H41H4!G3   + A  8!F2+8C G3q&4$4$*(& 4$"  / ; (810  ! (11RYRYsQX   +A  DW+BB  B!P2(L"C QXq/==///="q0-?7?-012447?-"Bq($&("&  : F (C9  + ((8   $( 11  8 E)#6  H+V+12  ::FH(C;5 with the simulation results chapter by sincere votingmanipulationusually The articles topics form a spiral. 1a) C-STVs winners always beat M-STVs whenever if the two systems rules elect different winners. 1b) When both C-STV and M-STV / systems are manipulable, C-STV often is harder to manipulate resist better because it usually requires a larger number of voters to  $( 10/? 6?ESpt$./|}BkVa  QRSmno  " # ? @  Q p  @ @ZV   ) * E H y {         J L X Z j l q r ~ q#%/0xz-1KMsy@A@\BHOY 01CDFGbruvz>EHPf 0;GV6ZA @@@WABv@AByz{  ( ) 0 J K M W Z ] d i j l m s y { | !!4!Y!_!v!w!!!!!@@ @R!!!!!!!!""""" 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Each rule requires an identical number of voters for manipulation in the set of elections with voting cycles. 2b) C-STV is more often impossible to manipulate resist than any other voting system except M-STV. But voters can always create a cycle and in 15% to 75% of elections that would change the winner. In some of that percentage the sincere Condorcet winner still could win the election by manipulating the elimination process. M-STV resists better only when it suffers exhibits fails the more serious failure of not electing a candidate with majority support. M-STV resists better only when it inherently errs more seriously by failing to elect the one candidate whom a majority of voters support over every other candidate one. (C-STV will do no worse than M-STV even if manipulation of these elections succeeds. It will elect the same candidate.)  =/P7 HARD DISK :4 Comparisons -:LaserWriter (K(FM n o p q r s 6CFGKRYklnwx_h!(,-9=>CEFGMRWekpqr"5STWXYZ[@ @ _SYSYRX   +A  EW)DB  B!Q2(L"C RX"02t0.>9>.022549>. ">.###### #  RX "D  ;G (D4  +((2   ( 4  8 E)%2  I+V+4  ;9G@(D:2 RXq4AA444A"!q'#%'"=# andexecute They rank thier favorite first and so cannot raise her any higher over the Condorcet winner., possibly,can no worse than MSTV. will elect the same candidate. IxIyIzxyze 2 insincere voters in group Ixse 2 plus the 4 voters under Iy s > But there will be cases where MSTV does not elect the Condorcet winner and is manipulabe; C-STV probably will be easier to manipulate. Voters under Ix and Iyting cycle. The 2 voters in Ix . Voters in Ix and Iy create a cycle and in 15% to 70sts better only when it suffers/ exhibits/ herto beatsuch manipulatorsneed wouldby chancewouldThus manipulationschance very Chandler proposed in 1985 that since voting cycles rarely occur by chance, we should suspect that a cycle indicates an attempted manipulation or at least a weak decission. This suggests that elections resulting in cycles a) Original poll  not of one toneD not of one toneandoordination ofmore than one y tactic not of one tone ost m manipulation not of one toneP &(*,-RSTV\cjqrsuwz[\_`mnopqrstuv@!nopqr+FP| X PH $@@@@@@@@@@@@@@@@FP| X PH $@@@@@FP| X$@$@$@$@@@@I@@I@@I@@I@@@@@@@@@@qrstuvrr+&&&&FP| X PH $@@@@@@@@@@@@@@FP| X PH $@@@@@@@FP| X PH $@@@@@@@@@@@@@@@@.|?#(V]n+nU x1>; 1; @ '6PLZls' P &(*,-RSTV\cjqrsuwz  =>?@BCEFHJKValxy}t@z. !!!M!z!'@+..../,/-/19[@JLCLcLwLxLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLMBMCMDMFMGMIMKMNMPMRMZMbMdMlMnMvMxMMMMMMN N N N N NNNNNN"N&N*N0N9NBNKNTN]NrNtNvNxNzN|NNNNNNNNNNNNNNNNNNNNNNNNNNOOOOOO#O%O+O1O6PiPjPPPPPPPPPPPPPPPPPPPPPPQQQQQQ QQQQQQQQDQEQGQHQJQMQOQQQZQ\Qbbhbbbbbbbbbbbbccccc ccccccccc!c%clcmcncpcqcscucxczc|cccccccccccdlmmmmnozoooooooppppp ppppp7p8p9p;pApHpOpVpWpXpZp\p_pjplpnpppqpspupzpppppppppppppppppppppppppppppqcqdqqqqqqqqqqqqqqqqqqqqqqqqqqqqqrrrr rrrrrrrrrr r!r"r#r$r%r'rrrsss2s3s4s5s6sUsVsWsYs`sbsdsfshsisjskslsnsts{ssssssssssssssssssssssssssssssssssssssssssssssssstHtItgthtttttttttttttttttttttttttttttttttttttttuuuuu u u uuuuuuuuuuuuu wy|#x#x #x  X  0    t p p p 0     t p p p 0 p p p p t p p p 0 p p p p t p p p 0 p p p p t p p p 0 p p p p tppp0pppp#x #x         @     @ t t t t @ t t t t @ t t t t @ t t t t @tttt#x#x#x #x #x#x#x #x5#x#x#x #x#x#x #x'#x#x#x#x#x #x #x#x#x #x&#x#x#x#x #x  h      ,  ,   ,  ,  ,  ,  ,  ,  ,  , #x                   #x#x                                        #x                   #x #x#x $ H      $ 8 8 $ 8 8 $ $ 8 8 $ 8 8 $ 8 8 $ 8 8 $ $8 8 $ 8 8 $ @           #x #x  h      ,  ,  ,  ,  ,  ,  ,  ,                    #x#x #x #x#x #x #x #x #x #x t     L   t p p p  L    t p p p  H    t p p p  H    t p p p  H    t p p p  H    tppp H   #x#x #x#x                                          #x#x #x#x                                                                    #x#x #x#x                                                          #x#x 36 !'70?LiP^(dmRp|[RSTUVWXYZ[\]^_`yw 02KLLtM0MNNXPPp_`zg\lmXmnnopbppqqrnqabcdefghijklmnopqrstuvwxyz{|}~"*\brHP(HPP  '=/P7 HARD DISK :4 Comparisons -:LaserWriter (K(||| 8C:C N N( !"#$+  !"#$-  !"#$CK \   stB BBB'B)B*B8B9B?B@BTBYBZCyC{CCCCCCCCCCCCCCCEEEEEEEEEEEFF F$FCFEFJFWFeFFFFFFFGG8GMGTGhGpGtGuGGGGGGGGGH HH!H%HmHtHxH{HIzIIIIILbLcNNNNNNPPPPPPSsSTT<TTTTTTTTTTTU U U UUUU$U2U:U;U<UBUCUDUEUFUGUUUUUUV*VXVYVwVWwWxWWWWXYYYYYZZZZZZZZZ3Z4Z@ZAZ_ZbZuZZZZZkkmPmQmmmnno*o+o9o:o;ooooopp;p_pppppppr'r(ssu u!v7v8wwxxxxxyRyTy}yyyyyyyzz z@zNzVzjzzz{{{&{P{{{{{{|J|T|Y|||K p qtuD>DCEFGD+CD,MDDEDDn(6CFGK!VYkEd:EeFClG1CnG9CwGCx:( 6:GK:RK:WX:}::::GMqGG,C -CHCIC9CSCgeCkCCDGGHHHHKKM:M>MCOOORSeS:O<s<:::<:<::< < <_hSCSCSCTT=CT?CT]ToCU^CCUyCCUCCUCpqr"5SWWWԀWThWj\Xjj YkZl6lD[lF\_`l l l m5 mY mz m m n\mm:m n\o n\p n\rs1tCuCuCCCCCCCDC FCOCiCsCCCCCCC CCCCKCCYC}CCCCC  nC v zq rC