VOTING TO ELECT A SINGLE CANDIDATE

1
VOTING TO ELECT A SINGLE CANDIDATE

• Single-Winner Elections

2
Single-Winner Elections

• Election of a unitary executive office.
• Election of a representative from a single-member
  district SMD
• Election of slate Presidential electors running
  on a (winner-take-all) general ticket/slate.

3
Binary Voting

• Just two options (so one winner and just one
  loser)
• Single-winner elections with just two candidates
• straight fight British terminology
• Yes/No voting
• referendums
• parliamentary voting

4
Kenneth Mays Theorem

• Choices for voters in straight fight between A
  and B
• vote for A
• vote for B
• abstain (if indifferent)
• Possible voting outcomes
• A is the winner
• B is the winner
• deadlock (no winner, hung electorate)

5
Mays Conditions (Reformulated)

• Anonymity (of voters)
• Neutrality (between options A and B)
• Resoluteness (no deadlock)
• Preliminary Theorem No voting system can be
  simultaneously Anonymous, Neutral, and Resolute.
• All voting systems considered here are Anonymous
  and Neutral.

6
Mays Conditions (cont.)

• Almost Resoluteness any deadlock is broken by
  any voter changing his vote.
• Non-Negative Responsiveness votes dont count
  negatively.
• Mays Theorem Anonymity Neutrality Almost
  Resoluteness Non-Negative Responsiveness ltgt
  Simple (Relative) Majority Rule

7
Strategyproofness

• Moreover, in a straight fight SMR is
  strategyproof
• That is, no voter can ever improve the outcome
  with respect to his or her true preferences by
  misreporting those preferences on a ballot.
• Voters will never regret voting sincerely or
  honestly.
• Sincere voting is Nash Equilibrium.
• However, in this respect SMR is not unusual in
  fact all non-negatively responsive voting systems
  are strategy-proof in a straight fight.

8
Three or More Candidates

• Once the number k of options/candidates exceeds
  two, all sorts of problems arise.
• Different (reasonable looking) voting
  procedures, all satisfying May-like conditions
  and equivalent to SMR in a straight fight, may
  produce different winners from the same
  preference profile.
• No voting procedure is strategyproof.
• No voting procedure is spoilerproof.
• This is essentially Arrows Theorem.
• One rationale for a two-party system is that it
  typically produces (something very close to)
  straight fights and therefore precludes these
  problems.

9
Preference Profiles

• With more than two candidates (k gt 2), voters
  preferences cannot be specified simply by listing
  their most preferred (top-ranked) candidates
  rather we must specify voters full preference
  ordering over all candidates (like the ice cream
  flavors).
• A collection of preference orderings, one for
  each voter is called a preference profile.
• We use British party labels to identify three
  candidates Labour, Liberal, and Conservative
  one of whom is to be elected. While there are
  six possible orderings of three candidates, we
  first consider a simple profile in which only
  three of these orderings are present and we
  indicate the popularity of each.
• We assume all have strict orderings (no
  indifference) and there are no ties.

10
Preference Profile 1

• of voters 46 20 34
• 1st pref. Labour Liberal Conserv.
• 2nd pref. Liberal Conserv. Liberal
• 3rd pref. Conserv. Labour Labour
• Simple Plurality Voting (SPV) first past the
  post or FPTP
• Plurality Ranking
• Candidates Votes Received ( First Preferences)
• Labour 46 votes (winner)
• Conservative 34 votes
• Liberal 20 votes
• Assuming sincere voting, SPV takes account of
  first preferences only.

11
Plurality vs. Majority Winner

• Given a preference profile with k gt 2
• A plurality winner is a candidate who has more
  first preferences than any other candidate.
• A plurality winner always exists in the absence
  of ties.
• A majority winner is a candidate who is the first
  preference of a majority of voters.
• Every majority winner is also a plurality winner,
  but the reverse is not true.
• There may not be a majority winner.

12
Plurality Plus Runoff (or Instant Runoff Voting
IRV)

• If there is no majority winner, there is a runoff
  between the top two candidates in the plurality
  ordering.
• Under IRV, Profile 1 would produce a runoff
  between Labour and Conservative first and second
  in the plurality ranking, which Conservative
  would win.

13
Approval Voting

• Voters can vote for (approve of) more than one
  candidate.
• The candidate with the most approval wins.
• Approval voting outcomes are indeterminate.
  Presumably a voter casts an approval vote for A
  and not for B only if the voters preference
  ordering ranks A over B no skipping.
• In Profile 1
• Labour wins if all voters cast only one vote.
• Conservative wins if only voters in the middle
  bloc cast two votes
• Liberal wins if all voters in the right bloc cast
  two votes or if all voters cast two votes.
• S. Brams and P. Fishburn, Approval Voting

14
Borda Point Voting

• Votes rank the candidates on the ballot.
• Candidates are awarded three points for each
  ballot on which they are ranked first, two points
  for each ballot on which they are ranked second,
  and one point for each ballot on which they are
  ranked third (if k 3).
• In general, m points, m-1 points, etc., when
  there are m candidates.
• Borda Ranking for Profile 1
• Liberal 220 points (winner)
• Labour 192 points
• Conservative 188 points

15
Condorcet Voting

• Votes rank the candidates on the ballot.
• Examine all pairs of candidates and see who wins
  each straight fight.
• For Profile 1
• Liberal vs. Conservative Liberal wins by 66-34
• Conservative vs. Labour Conservative wins by
  54-46
• Liberal vs. Labour Liberal wins by 54-46
• Assemble the Majority (or Condorcet) Ranking
• 1st pref. Liberal (Condorcet Winner)
• 2nd pref. Conservative
• 3rd pref. Labour (Condorcet Loser)
• Precisely opposite of Plurality Ranking (based on
  1st prefs. only) and different from Borda Ranking
  (also based on full rankings)

16
Condorcet Winners

• A Condorcet winner is a candidate who can beat
  every other candidate in a straight fight.
• A Condorcet loser is a candidate who is beaten by
  every other candidate in a straight fight.
• A majority winner is always a Condorcet winner,
  but the reverse is not true.
• A plurality winner may not be a Condorcet winner.
• A Condorcet winner may not be a plurality winner.
• Indeed, a Condorcet winner may have the fewest
  first preferences (e.g., Liberal in Profile 1).

17
Condorcet Voting (cont.)

• Moreover, Condorcet Voting appears to be
• Strategyproof, because it is built on Simple
  Majority Rule, which is strategyproof and
• Spoilerproof, because (for example), regard-less
  of whether Nader is a candidate or not, Bush is
  the Condorcet winner only if he beats Gore in a
  straight fight.
• So what about Arrows Theorem?

18
Problem There may be no Condorcet Winner

• This assertion seems puzzling because every
  ranking has a highest ranked element.
• But there may be no Majority Ranking.

19
Preference Profile 2

• of voters 46 20 34
• 1st pref. Labour Liberal Conserv.
• 2nd pref. Liberal Conserv. Labour
• 3rd pref. Conserv. Labour Liberal
• First preferences are unchanged from Profile 1,
  so the plurality winner is unchanged.
• As before, there is no majority winner.
• Conservative remains the Plurality Runoff winner.
• Labour becomes the Borda point winner.
• Approval voting remains indeterminate.

20
Cyclical Majorities

• Re-examine the straight fights
• Liberal vs. Conservative Liberal wins by 66-34
• Conservative vs. Labour Conservative wins by
  54-46
• Labour vs. Liberal Labour wins by 80-20
• There is no majority ranking, no Condorcet
  Winner, and no Condorcet Loser.
• Instead we have a cyclical majority that behaves
  like the even stranger ice cream customer.
• In general, Condorcet Winners may not exist and
  Condorcet Voting is not a proper voting system,
  so Arrows Theorem stands.

21
Preference Profile 3

• of voters 35
  33 32
• 1st pref. B C D
• 2nd pref. A A A
• 3rd pref. C D B
• 4th pref. D B C
• Example of a socially divided society (e.g.,
  Shiites, Sunnis, and Kurds in Iraq) Candidate A
  is the alliance (cross-community) candidate.
• Candidate A is the Condorcet Winner even though A
  has no first preferences.
• Candidate A is the Condorcet Winner even though
  the is a majority cycle among the other
  candidates.
• Side point If A, B, C, and D are parties, the
  Alliance Party A wins no seats under list-PR.

22
Condorcet Consistency

• A voting rule is Condorcet consistent if, given
  sincere voting, it always selects the Condorcet
  winner when one exists.
• Previous examples showed that, given Profile 1,
  Liberal may fail to win under each of the other
  voting rules discussed, so none of them is
  Condorcet consistent.
• Condorcet voting is obviously Condorcet
  consistent but, since it is does not always
  select a winner, it cannot be deemed a
  full-fledged voting rule.

23
Parliamentary (Yes/No) Voting

• There are options A, B, C, D, .
• Voting is by a sequence of binary votes taken in
  some fixed order (say alphabetical)
• (1) A vs. B
• (2) winner of (1) vs. C
• (3) and so forth
• If there is a Condorcet Winner, it can never be
  knocked out, so CW wins regardless of the voting
  order.
• If there is a majority cycle and no CW, winner is
  determined by the voting order (later entry is
  advantageous).

24
Single-Peaked Preferences

• To say that majority cycles may exist is not to
  say that they typically are present.
• Indeed, if preferences are structured in a simple
  way by ideology (or otherwise), cycles cannot
  occur.
• In British politics, the three major parties are
  generally perceived to be ideologically ranked
  from left to right in the following manner
• More leftwing Labour
• Relatively centrist Liberal
• More rightwing Conservative

25
Single-Peaked Preferences (cont.)

• Admissible Orderings Inadmissible
• Leftwingers Centrists
  Rightwingers Orderings
• 1st pref. Lab Lib Lib Con Con Lab
• 2nd pref. Lib Lab Con Lib Lab Con
• 3rd pref. Con Con Lab Lab Lib Lib
• Why the name single-peaked?
• In diagrams below, L leftist, C centrist, and
  R rightist

26
Single-Peaked Preferences (cont.)

• Note the strength of the centrist (Liberal)
  candidate in the admissible orderings.
• While it may be that few voters most prefer the
  centrist, no one likes the centrist least.
• The centrist candidate must be the Condorcet
  Winner unless a majority of voters have the
  leftwing or rightwing ordering.
• In other words, the centrist candidate fails to
  be the Condorcet Winner only if one of the
  extreme candidates is a majority winner.
• In the general case, if all voters can be ranked
  from most leftwing to most rightwing with respect
  to their first preferences,
• no cyclical majority occurs
• some position on the ideological spectrum is the
  Condorcet Winner and
• that CW position corresponds to the first
  preference of the median voter, such that no more
  than half the voters are more leftwing and no
  more than half are more rightwing (Duncan Black,
  Theory of Committees and Elections.
• The Hotelling-Downs theory of electoral
  competition (to be discussed later) states that
  two competing vote-seeking parties or candidates
  achieve equilibrium only when both adopt the
  position that corresponds to the first preference
  of the median voter.

27
Strategic Voting under Plurality Rule

• Any voting rule with three or more candidates may
  give some voters incentives to vote otherwise
  than sincerely.
• Consider Profile 1 again.
• of voters 46 20 34
• 1st pref. Labour Liberal Conserv.
• 2nd pref. Liberal Conserv. Liberal
• 3rd pref. Conserv. Labour Labour
• Labour wins under Plurality Voting if voters are
  sincere.
• But a majority of 54 voters prefer both other
  candidates to Labour.
• If they all vote for the same other candidate,
  that candidate wins, an outcome they all prefer
  to a Labour victory.
• But doing this requires some voters among the 54
  to vote insincerely, i.e., for their second
  preferences.
• Thus simple Plurality Voting can encourage what
  the British call tactical voting and most
  political scientists call strategic voting, i.e.,
  non-sincere voting.

28
Strategic Voting under Plurality Rule (cont.)

• But how will the 54 voter majority coordinate
  their votes? Will they all vote for Liberal or
  for Conservative?
• While all 54 voters prefer to see Labour
  defeated, they disagree as to how to defeat him,
  i.e., by voting Conservative or by voting
  Liberal.
• It is generally believed that, in practice,
  tactical voting in Britain mostly leads Liberal
  supporters to shift their votes tactically to
  their second-preference (Labour or Conservative)
  candidate, because they typically observe
  pre-election polls showing Liberal trailing well
  behind both other candidates, and they therefore
  conclude that a Liberal vote is wasted and that
  they should vote for the one of the two leading
  (non-Liberal) candidates that they prefer.
• This can happen even though Liberal is the
  Condorcet winner, reflecting the fact that polls
  (almost always) ask only about first preferences
  and Liberal's great strength lies in second
  preferences.
• If Liberal supporters find Labour and
  Conservative to be equally objectionable, they
  have no incentive to vote tactically.
• If pre-election polls show something close to a
  tie for second place (or a three-way tie),
  tactical voting becomes far more conjectural.

29
Strategic Voting under Runoff or IRV

• Preference Profile 1
• of voters 46 20 34
• 1st pref. Labour Liberal Conserv.
• 2nd pref. Liberal Conserv. Liberal
• 3rd pref. Conserv. Labour Labour
• Under Plurality Runoff or IRV, the 46 voters
  who most prefer Labour would do better by ranking
  Liberal first, as this assures a Liberal victory
  (without a runoff), which outcome they prefer to
  the Conservative victory that otherwise results.
  
• Moreover, other voters have no countermoves
  available. No strategic vote is available to 34
  voters whose first preference is Conservative,
  and the 20 voters whose first preference is
  Liberal are already getting their first
  prefer-ence.

30
Strategic Voting Under Borda Point Voting

• Given Profile 1, no voters can change their Borda
  score ballots in a way that improves the outcome
  for them.
• Profile 2
• of voters 46 20 34
• 1st pref. Labour Liberal Conserv.
• 2nd pref. Liberal Conserv. Labour
• 3rd pref. Conserv. Labour Liberal
• Given Profile 2, if the bloc of 20 ranks
  Conservative first and the bloc of 34 ranks
  Labour third, then Conservative gets the most
  Borda points (208 vs. 200 for Liberal and 192 for
  Labour), an outcome all 54 such voters prefer to
  victory by the sincere Borda winner Labour.

31
Strategic Voting Under Borda (cont.)

• Preference Profile 3 4 in Handout
• 46 54
• 1st pref. Labour Conservative
• 2nd pref. Liberal Labour
• 3rd pref. Conservative Liberal
• Labour wins if voting is sincere (demonstrating
  that Borda Point Voting can deny victory to a
  majority winner).
• But the 54 Conservative-preferring voters can
  elect Conservative if they (insincerely) push
  Labour down to third place on their ballots.
• In turn, the 46 Labour-preferring voters can
  counteract this by pushing Liberal to the top of
  their ballots (the resulting Liberal victory
  being preferable to Conservative).
• Note that if strategic manipulation stops at this
  point (though it need not), Liberal is elected
  even though everyone prefers Labor to Liberal.
• And things can get worse.

32
Borda Strategy Turkey Raising

• There are three candidates a more or less
  reasonable Democrat D, a more or less reasonable
  Republican R, and a real turkey T. Everyone
  one ranks T last, except two deranged T
  supporters. The profile is
• 50 voters 48 voters 1 voter 1
  voter
• D R T T
• R D D R
• T T R D
• If everyone votes sincerely, the Borda Point
  totals are D249, R247, and T104.
• Anticipating this defeat, Republican voters
  caucus and notice an interesting feature of Borda
  Point Voting it can pay voters to engage in
  turkey raising, i.e., to strategically raise
  the turkey in their ballot rankings, so as to
  push the rival serious candidate down in their
  rankings and increase the point spread between
  the two.

33
Turkey Raising (cont.)

• Suppose the Republicans strategically modify all
  their ballots so as to produce the following
  ballot profile
• 50 voters 48 voters 1 voter 1
  voter
• D R T T
• R T D R
• T D R D
• The point totals would then be D201, R247, and
  T152.
• Democrats also notice this feature of Borda
  Voting and, concerned that Republicans may engage
  in turkey raising, they engage in some turkey
  raising of their own in order to counteract the
  anticipated Republican stratagem. So the final
  ballot profile is
• 50 voters 48 voters 1 voter 1
  voter
• D R T T
• T T D R
• R D R D
• The final point scores are D 201, R 197, and
  T 202. May the best turkey win!

34
Spoiler Effects

• A sincere electorate using Plurality Voting may
  behave exactly the confused ice cream customer.
• Preference Profile 1
• of voters 46 20 34
• 1st pref. Labour Liberal Conserv.
• 2nd pref. Liberal Conserv. Liberal
• 3rd pref. Conserv. Labour Labour
• Conservative beats Labour in a straight fight,
  but Labour wins if Liberal enters the election.
  So Liberal is a spoiler to Conservative.
• Likewise, Liberal beats Labour in a straight
  fight, but Labour wins if Conservative enters the
  election. So Conservative is also a spoiler to
  Liberal.
• Note that the effect of the spoilers entry is to
  elect the last preference of the spoilers
  supporters, so the spoilers entry is
  self-defeating.
• Note that, in this profile, Labour cannot be a
  spoiler, because if Labour enters what had been a
  Liberal-Conservative straight fight, Labour wins.

35
Spoiler Effects (cont.)

• Spoiler effects may be mitigated by strategic
  voting.
• Duvergers Law Single-Winner elections with
  Simple Plurality Voting tend to produce two-party
  systems and straight fights Strategic voting to
  mitigate spoiler effects is one factor that
  drives Duvergers Law.
• Dont waste your vote on a hopeless third
  candidate.
• Candidate entry deterrence is the other,
  probably more important, factor that drives
  Duvergers Law.
• Dont run as a third candidate, you will spoil
  the chances of the preferable of the two major
  candidates.
• Multi-Winner elections no elected executives
  with any variant of Proportional Representation
  PR sustains multiparty systems. Other half of
  Duvergers Law

36
Spoiler Effects under IRV

• Plurality Runoff/IRV is sometimes advocated on
  the grounds that it precludes the spoiler effects
  that characterize Simple Plurality.
• Plurality Runoff/IRV is an improvement over
  Simple Plurality in this respect.
• Under IRV, a single third candidate (such as
  Nader) with little first-preference support
  cannot act as a spoiler in what is essentially a
  straight fight between two major candidates,
  because the runoff will become precisely that
  straight fight.
• However, if there are many candidates and/or
  first preferences are dispersed, Plurality
  Runoff/IRV is subject to spoiler effects.

37
Two Variants of IRV

• There are (at least) variants of IRV.
• They are equivalent if there are just three
  candidates but are distinct (and may produce
  different winners) if there are more than three
  candidates.
• The first variant mimics Plurality Runoff.
• If there is no majority winner, all candidates
  except the leading and second-place candidate in
  the plurality ranking are simultaneously
  eliminated.
• The ballots of all eliminated candidates are
  trans-ferred to one or other surviving candidate
  on the basis of lower preferences.
• The surviving candidate with the most (original
  plus transferred) ballots is elected.

38
Two Variants of IRV (cont.)

• The second variant is distinct from plurality
  runoff.
• If there is no majority winner, the candidate
  with the fewest first preference ballots is
  eliminated.
• The ballots of the eliminated candidate are
  trans-ferred to one of the surviving candidate on
  the basis of second preferences.
• If there is still no majority winner, the
  surviving candi-date with the fewest (original
  plus transferred) ballots is eliminated and the
  ballots are transferred on the basis of second or
  lower preferences.
• And so forth until there is a majority winner
  (which necessarily occurs once all candidates but
  two have been eliminated.

39
Two Variants of IRV (cont.)

• The second variant of IRV is also called the
  Alternative Vote.
• It is the single-winner special case of a
  multi-winner voting system called the Single
  Transferable Vote (STV).
• STV is used in small multi-member districts
  (MMDs).
• It produces approximately proportional
  representation of groups among the winners, even
  if those groups are not political parties.
• contrast with List-PR
• STV is used to elect
• the Irish Dail (Parliament)
• the Australian House of Representative
• the Cambridge MA City Council

40
Spoiler effects under Plurality Runoff (and 1st
IRV variant)

• When there are many candidates, the Plurality
  Runoff and the first variant of IRV are subject
  to spoiler effects in precisely the same manner
  as Simple Plurality Voting, with respect to the
  question of which two candidates will survive
  into the runoff.
• This is illustrated by the 2002 French
  Presidential election (Two Round or Plurality
  Runoff).

41

• Left splinter candidates spoiled Jospins
  chance to get into the second round runoff
  against Chirac.
• However, if the second AV variant of IRV had
  been in used
• ballots for left splinter candidates would have
  (presumably) transferred to Jospin
• few ballot would have transferred to Le Pen and
• Jospin would have gotten into the runoff and
  might have won.

42
Would Runoff/IRV Lead to a Proliferation of
Presidential Candidates?
43
Spoiler Effects under 2nd IRV Variant (AV)

• However, spoiler effects also exist under the
  second IRV variant. This is illustrated by
  Preference Profile 1 with just three candidates
  (in which case the two variants are equivalent)
• of voters 46 20 34
• 1st pref. Labour Liberal Conserv.
• 2nd pref. Liberal Conserv. Liberal
• 3rd pref. Conserv. Labour Labour
• Liberal wins a straight fight with Conservative,
  but Liberal does not even make it into the runoff
  if Labour enters the field. So Labour is a
  spoiler to Liberal under IRV.
• This is not a distinctive flaw in Plurality
  Runoff (or IRV) because, as previously noted, the
  problem is unavoid-able with three or more
  candidates.

44
Negative Responsiveness under Plurality Runoff
(or IRV)

• Plurality Runoff (or IRV) has another flaw that
  is distinctive (and avoidable).
• Plurality Runoff (or IRV) can respond negatively
  when a candidates position in a preference (or
  ballot) profile becomes more favorable put
  otherwise, it can punish a candidate for gaining
  more support.
• This sometimes called monotonicity failure.
• It is a violation of Mays Non-Negative
  Responsive-ness condition

45
Negative Responsiveness under Plurality Runoff or
IRV (cont.)

• Original Preference Profile 4
  Revised Preference Profile 4
• 35 10 25 30
  35 10 25 30
• A B B
  C A A B C
• B A C A B
  B C A
• C C A B
  C C A B
• Prior to the election, a poll indicates that
  voting intentions those shown in Original
  Preference Profile 4. Candidate A is pleased
  with this information, because it projects that A
  and B will go into the runoff, which A will win.
• However, A doesnt want to take any chances and
  urges his supporters to go out and drum up still
  more support for A. As supporters are
  successful, transforming the original profile
  into the revised profile, in which 10 voters who
  previously preferred B to A now prefer A to B.
  (No other preferences have changed.)
• As a result of this successful campaign, A loses
  the election.

46
IRV and the No Show Paradox

• Here is a related peculiarity of Plurality
  Runoff or IRV.
• Preference Profile 5
• 5 6 4 2 B C A A C B B B
  A A C C
• The preference profile is as shown above, but the
  two individuals with the bracketed preference
  orderings fail to vote.
• The election outcome is determined by the
  remaining 15 voters. Candidates B and C are
  paired in a runoff, which B wins.
• This is somewhat disappointing for the two
  individuals who failed to vote, in that their
  second preference won.
• They regret their failure to get to the polls and
  wonder whether their first preference A might
  have won if they had not failed to vote.
• It can be checked that, if they had gotten to the
  polls and voted according to their preferences, C
  would have won (so the outcome would have been
  worse, not better, for them).

47
Clone Candidates

• When I was 12 years old I was nominated to be
  treasurer of my class at school. A girl named
  Michelle was also nominated. I relished the
  prospect of being treasurer, so I made a quick
  calculation and nomi-nated Michelles best
  friend, Charlotte. In the ensuing election, I
  received 13 votes, Michelle received 12, and
  Charlotte received 11, so I became treasurer.
  T.N. Tideman
• Consider the following preference profile, in
  which a Republican minority is united behind a
  single candidate R but the Democratic majority is
  split between the two clone candidates D1 and
  D2.
• Preference Profile 6
• Democrats Republicans
• 35 25 25 15
• D1 D2 R R
• D2 D1 D1 D2
• R R D2 D1

48
Clone Candidates (cont.)

• Clones are candidates who very similar in terms
  of their ideology, issue positions, etc. and are
  therefore adjacent in all voters preference
  rankings.
• Simple Plurality is notorious for penalizing
  clone candi-dates.
• In this case, the Republican candidate wins due
  to the Demo-cratic split, even though R is the
  Condorcet loser and would be beaten by both D1
  and D2 in straight fights.
• D1 and D2 are spoilers against each other.
• It is precisely the expectation of such outcomes
  under Simple Plurality voting that leads to party
  formation and party discipline.
• The Democrats and the girls have a huge
  incentive to hold a prior nominating convention
  or primary to choose between D1 and D2 and then
  send just one of the two clones forward against
  the Republican.
• Given the preference profile above, D1 would win
  the nomination and then the general election.

49
Plurality Runoff or IRV and Clones

• Are there voting rules that can reduce,
  eliminate, or even reverse the self-defeating
  effect of run-ning clone candidates?
• Given Profile 6, Plurality Runoff (instant or
  other-wise) solves the clone problem.
• The first-round election functions as the
  (Democratic) primary (except that Republicans
  also vote in this primary).
• The runoff functions as the general election in
  which the Democratic majority gets its way.
• If there are four or more candidates, Plurality
  Runoff or IRV does not treat clones so well
  and, as we have seen, it is subject to other
  problems in addition.

50
Approval Voting and Clones

• Brams and Fishburn advocate Approval Voting as a
  desirable a voting rule that (among other things)
  does not punish clones.
• In Profile 6, presumably (almost all) Democrats
  would vote for both D1 and D2, one of whom would
  be elected.
• By not penalizing clones, AV does not encourage
  party formation or party unity.
• For this reason, many political scientists are
  more inclined to support AV for primary elections
  and non-partisan elections than for partisan
  general elections.

51
Double-Vote List-PR and Clones

• A variation of one type of party-list PR
  (Propor-tional Representation) system is another
  voting method that does not penalize clones who
  have the same party affiliation.
• In a district that elects m candidates, each
  voter votes for m candidate, but these vote
  counts in two ways
• first, as a party vote to determine which party
  wins the election and
• second, as a candidate vote to determine which
  candidate(s) of the winning party is elected. In
  the profile above (with m 1), D1 would be
  elected.

52
Borda Point Voting and Clones

• Perhaps surprisingly, Borda Point Voting actually
  rewards the running of clones.
• Suppose that there are two candidates and
  Republicans are again in the minority.
• Preference Profile 7A
• 60 voters 40 voters
• D R1
• R1 D
• With just two candidates, the Borda point rule is
  identical to Plurality Voting (and SMR), so the
  Republican candidate R1 loses.

53
Borda Point Voting and Clones (cont.)

• But, if Borda Voting is in use, the Republicans
  can reverse this outcome by nominating an
  additional clone candidate R2 whom everyone sees
  as identical to R1 with respect to issues and
  ideology but inferior with respect to (lets say)
  personal qualities.
• Preference Profile 8A
• 60 voters 40 voters
• D R1
• R1 R2
• R2 D
• Democrats can counteract this Republican
  stratagem by strategi-cally ranking R2 above R1.
• Alternatively, they can counteract it by running
  their own clone.
• Borda voting is highly susceptible to strategic
  maneuvers of this sort (which, moreover, have the
  effect of expanding the candidate field rather
  than winnowing it down in the manner of Plurality
  Rule).
• Also recall turkey raising under Borda

54
Overall Conclusion

• Two-candidate elections (straight fights) are
  clean and simple.
• Elections with three or more candidates are
  complex and inevitably quirky.