A
Condorcet method is any singlewinner
election method that meets the
Condorcet criterion, that is, which
always selects the Condorcet winner, the candidate who would beat
each of the other candidates in a runoff election, if such a
candidate exists. In modern examples, voters rank candidates in
order of preference. There are then multiple, slightly differing
methods for calculating the winner, due to the need to resolve
circular
ambiguities—including the
KemenyYoung method,
Ranked Pairs, and the
Schulze method.
Condorcet methods are named for the eighteenthcentury
mathematician and
philosopher Marie Jean Antoine Nicolas
Caritat, the
Marquis de
Condorcet.
Ramon Llull had devised
one of the first Condorcet methods in 1299, but this method is
based on an iterative procedure rather than a
ranked ballot.
Summary
 Rank the candidates in order (1st, 2nd, 3rd, etc.) of
preference. Tie rankings, which express no preference between the
tied candidates, are allowed.
 For each ballot, compare the ranking of each candidate on the
ballot to every other candidate, one pair at a time (pairwise), and
tally a "win" for the higherranked candidate.
 Sum these wins for all ballots cast, maintaining separate
tallies for each pairwise combination.
 The candidate who wins every one of their pairwise contests is
the most preferred over all other candidates, and hence the winner
of the election.
 In the event no single candidate wins all pairwise contests,
use a resolution method described below.
A particular point of interest is that it is possible for a
candidate to be the most preferred overall without being the first
preference of
any voter. In a sense, the Condorcet method
yields the "best compromise" candidate, the one that the largest
majority will find to be least disagreeable, even if not their
favorite.
Definition
A Condorcet method is a voting system that will always elect the
Condorcet winner; this is the candidate whom voters prefer to each
other candidate, when compared to them one at a time. This
candidate can easily be found by conducting a series of pairwise
comparisons, using the basic procedure described in this article.
The family of Condorcet methods is also referred to collectively as
Condorcet's method. A voting system that always
elects the Condorcet winner when there is one is described by
electoral scientists as a system that satisfies the
Condorcet
criterion.
In certain circumstances an election has no Condorcet winner. This
occurs as a result of a kind of tie known as a 'majority rule
cycle', described by
Condorcet's
paradox. The manner in which a winner is then chosen varies
from one Condorcet method to another. Some Condorcet methods
involve the basic procedure described below, coupled with a
Condorcet completion method—a method used to find a winner when
there is no Condorcet winner. Other Condorcet methods involve an
entirely different system of counting, but are classified as
Condorcet methods because they will still elect the Condorcet
winner if there is one.
It is important to note that not all single winner,
preferential voting systems are Condorcet
methods. For example,
instantrunoff voting and the
Borda count do not satisfy the Condorcet
criterion.
Basic procedure
Voting
In a Condorcet election the voter ranks the list of candidates in
order of preference. So, for example, the voter gives a '1' to
their first preference, a '2' to their second preference, and so
on. In this respect it is the same as an election held under
nonCondorcet methods such as
instant runoff voting or the
single transferable vote. Some
Condorcet methods allow voters to rank more than one candidate
equally, so that, for example, the voter might express two first
preferences rather than just one.
Usually, when a voter does not give a full list of preferences they
are assumed, for the purpose of the count, to prefer the candidates
they have ranked over all other candidates. Some Condorcet
elections permit
writein
candidates but, because this can be difficult to implement,
software designed for conducting Condorcet elections often do not
allow this option.
Finding the winner
The count is conducted by pitting every candidate against every
other candidate in a series of imaginary oneonone contests. The
winner of each pairing is the candidate preferred by a majority of
voters. The candidate preferred by each voter is taken to be the
one in the pair that the voter ranks highest on their ballot paper.
For example, if Alice is paired against Bob it is necessary to
count both the number of voters who have ranked Alice higher than
Bob, and the number who have ranked Bob higher than Alice. If Alice
is preferred by more voters then she is the winner of that pairing.
When all possible pairings of candidates have been considered, if
one candidate beats every other candidate in these contests then
they are declared the Condorcet winner. As noted above, if there is
no Condorcet winner a further method must be used to find the
winner of the election, and this mechanism varies from one
Condorcet method to another.
Pairwise counting and matrices
Condorcet methods use pairwise counting. For each possible pair of
candidates, one pairwise count indicates how many voters prefer one
of the paired candidates over the other candidate, and another
pairwise count indicates how many voters have the opposite
preference. The counts for all possible pairs of candidates
summarize all the preferences of all the voters.
Pairwise counts are typically displayed in matrices such as those
below. In these matrices each row represents each candidate as a
'runner', while each column represents each candidate as an
'opponent'. The cells at the intersection of rows and columns each
show the result of a particular pairwise comparison. Certain cells
are left blank because it is impossible for a candidate to be
compared with him or herself.
Imagine there is an election between four candidates: A, B, C and
D. The first matrix below records the preferences expressed on a
single ballot paper, in which the voter's preferences are (B, C, A,
D); that is, the voter ranked B first, C second, A third, and D
fourth. In the matrix a '1' indicates that the runner is preferred
over the 'opponent', while a '0' indicates that the runner is
defeated.

Opponent 
A 
B 
C 
D 
R
u
n
n
e
r 
A 
— 
0 
0 
1 
B 
1 
— 
1 
1 
C 
1 
0 
— 
1 
D 
0 
0 
0 
— 
A '1' indicates
that the runner is preferred over the opponent; a '0' indicates
that the runner is defeated. 
Matrices of this kind are useful because they can be easily added
together to give the overall results of an election. The sum of all
ballots in an election is called the sum matrix. Suppose that in
the imaginary election there are two other voters. Their
preferences are (D, A, C, B) and (A, C, B, D). Added to the first
voter, these ballots would give the following sum matrix:

Opponent 
A 
B 
C 
D 
R
u
n
n
e
r 
A 
— 
2 
2 
2 
B 
1 
— 
1 
2 
C 
1 
2 
— 
2 
D 
1 
1 
1 
— 
When the sum matrix is found, the contest between each pair of
candidates is considered. The number of votes for runner over
opponent (runner,opponent) is compared with the number of votes for
opponent over runner (opponent,runner). It is then possible to find
the Condorcet winner. In the sum matrix above it can be seen that A
is the Condorcet winner because A beats every other candidate. When
there is no Condorcet winner Condorcet completion methods, such as
Ranked Pairs and the Schulze method, use the information contained
in the sum matrix to choose a winner.
Cells marked '—' in the matrices above have a numerical value of
'0', but a dash is used since candidates are never preferred to
themselves. The first matrix, that represents a single ballot, is
inversely symmetric: (runner,opponent) is ¬(opponent,runner). Or
(runner,opponent) + (opponent,runner) = 1. The sum matrix has this
property: (runner,opponent) + (opponent,runner) = N for N voters,
if all runners were fully ranked by each voter.
An example
To find the Condorcet winner every candidate must be matched
against every other candidate in a series of imaginary oneonone
contests. In each pairing the winner is the candidate preferred by
a majority of voters. When results for every possible pairing have
been found they are as follows:
Pair 
Winner 
Memphis (42%) vs. Nashville (58%) 
Nashville 
Memphis (42%) vs. Chattanooga (58%) 
Chattanooga 
Memphis (42%) vs. Knoxville (58%) 
Knoxville 
Nashville (68%) vs. Chattanooga (32%) 
Nashville 
Nashville (68%) vs. Knoxville (32%) 
Nashville 
Chattanooga (83%) vs. Knoxville (17%) 
Chattanooga 
The results can also be shown in the form of a matrix:

A 
Memphis 
Nashville 
Chattanooga 
Knoxville 
B 
Memphis 

[A] 58%
[B] 42%

[A] 58%
[B] 42%

[A] 58%
[B] 42%

Nashville 
[A] 42%
[B] 58%


[A] 32%
[B] 68%

[A] 32%
[B] 68%

Chattanooga 
[A] 42%
[B] 58%

[A] 68%
[B] 32%


[A] 17%
[B] 83%

Knoxville 
[A] 42%
[B] 58%

[A] 68%
[B] 32%

[A] 83%
[B] 17%

Ranking: 
4th 
1st 
2nd 
3rd 
 [A] indicates voters who preferred the candidate listed in the
column caption to the candidate listed in the row caption
 [B] indicates voters who preferred the candidate listed in the
row caption to the candidate listed in the column caption
 "Ranking" is found by repeatedly removing the Condorcet winner
(it is not necessary to find these rankings).
As can be seen from both of the tables above, Nashville beats every
other candidate. This means that Nashville is the Condorcet winner.
Nashville will thus win an election held under any possible
Condorcet method.
While any Condorcet method will elect Nashville as the winner, if
instead an election based on the same votes were held using
firstpastthepost or
instantrunoff voting, these systems
would select Memphis and Knoxville respectively. This would occur
despite the fact that most people would have preferred Nashville to
either of those "winners". Condorcet methods make these preferences
obvious rather than ignoring or discarding them.
Circular ambiguities
As noted above, sometimes an election has no Condorcet winner
because there is no candidate who is preferred by voters to all
other candidates. When this occurs the situation is known as a
'majority rule cycle', 'circular ambiguity' or 'circular tie'. This
situation emerges when, once all votes have been added up, the
preferences of voters with respect to some candidates form a circle
in which every candidate is beaten by at least one other candidate.
For example, if there are three candidates, Andrea, Carter and
Delilah, there will be no Condorcet winner if voters prefer Andrea
to Carter and Carter to Delilah, but also Delilah to Andrea.
Depending on the context in which elections are held, circular
ambiguities may or may not be a common occurrence. Nonetheless
there is always the possibility of an ambiguity, and so every
Condorcet method must be capable of determining a winner when this
occurs. A mechanism for resolving an ambiguity is known as
ambiguity resolution or Condorcet completion method.
Circular ambiguities arise as a result of the
voting paradox—the result of an election can
be intransitive (forming a cycle) even though all individual voters
expressed a transitive preference. In a Condorcet election it is
impossible for the preferences of a single voter to be cyclical,
because a voter must rank all candidates in order and can only rank
each candidate once, but the paradox of voting means that it is
still possible for a circular ambiguity to emerge.
The idealized notion of a
political
spectrum is often used to describe political candidates and
policies. This means that each candidate can be defined by her
position along a straight line, such as a line that goes from the
most right wing candidates to the most left wing, with centrist
candidates occupying the middle. Where this kind of spectrum exists
and voters prefer candidates who are closest to their own position
on the spectrum there is a Condorcet winner (Black's
SinglePeakedness Theorem). Real political spectra, however, are at
least two dimensional.
In Condorcet methods, as in most electoral systems, there is also
the possibility of an ordinary tie. This occurs when two or more
candidates tie with each other but defeat every other candidate. As
in other systems this can be resolved by a random method such as
the drawing of lots. Ties can also be settled through other methods
like seeing which of the tied winners had the most first choice
votes, but this and some other nonrandom methods may reintroduce
a degree of tactical voting, especially if voters know the race
will be close.
The method used to resolve circular ambiguities is the main
difference between Condorcet methods. There are countless ways in
which this can be done, but every Condorcet method involves
ignoring the majorities expressed by voters in at least some
pairwise matchings.
Condorcet methods fit within two categories:
 Twomethod systems, which use a separate
method to handle cases in which there is no Condorcet winner
 Onemethod systems, which use a single method
that, without any special handling, always identifies the winner to
be the Condorcet winner
Twomethod systems
One family of Condorcet methods consists of systems that first
conduct a series of pairwise comparisons and then, if there is no
Condorcet winner, fall back to an entirely different, nonCondorcet
method to determine a winner. The simplest such methods involve
entirely disregarding the results of pairwise comparisons. For
example, the Black method chooses the Condorcet winner if it
exists, but uses the
Borda count instead
if there is an ambiguity (the method is named for
Duncan Black).
A more sophisticated twostage process is, in the event of an
ambiguity, to use a separate voting system to find the winner but
to restrict this second stage to a certain subset of candidates
found by scrutinizing the results of the pairwise comparisons. Sets
used for this purpose are defined so that they will always contain
only the Condorcet winner if there is one, and will always, in any
case, contain at least one candidate. Such sets include the
 Smith set: The
smallest nonempty set of candidates in a particular election such
that every candidate in the set can beat all candidates outside the
set. It is easily shown that there is only one possible Smith set
for each election.
 Schwartz set: This
is the innermost unbeaten set, and is usually the same as the Smith
set. It is defined as the union of all possible sets of candidates
such that for every set:
 Every candidate inside the set is pairwise unbeatable by any
other candidate outside the set (i.e., ties are allowed).
 No proper (smaller) subset of the set fulfills the first
property.
 Landau set (or
uncovered set or Fishburn set):
the set of candidates, such that each member, for every other
candidate (including those inside the set), either beats this
candidate or beats a third candidate that itself beats the
candidate that is unbeaten by the member.
One possible method is to apply
instantrunoff voting to the
candidates of the Smith set. This method has been described as
'Smith/IRV'.
Singlemethod systems
Some Condorcet methods use a single procedure that inherently meets
the Condorcet criteria and, without any extra procedure, also
resolves circular ambiguities when they arise. In other words,
these methods do not involve separate procedures for different
situations. Typically these methods base their calculations on
pairwise counts. These methods include:
 Copeland's
method: This simple method involves electing the
candidate who wins the most pairwise matchings. However, it often
produces a tie.
 KemenyYoung
method: This method ranks all the choices from most
popular and secondmost popular down to least popular.
 Minimax: Also
called 'Simpson', 'SimpsonKramer', and 'Simple Condorcet', this
method chooses the candidate whose worst pairwise defeat is better
than that of all other candidates. A refinement of this method
involves restricting it to choosing a winner from among the Smith
set; this has been called 'Smith/Minimax'.
 Nanson's
method
 Dodgson's
method
 Ranked Pairs: This
method is also known as 'Tideman', after its inventor Nicolaus Tideman.
 Schulze method:
This method is also known as 'Schwartz sequential dropping' (SSD),
'cloneproof Schwartz sequential dropping' (CSSD), 'beatpath
method', 'beatpath winner', 'path voting' and 'path winner'.
Ranked Pairs and Schulze are procedurally in some sense opposite
approaches (although they very frequently give the same results):
 Ranked Pairs (and its variants) starts with the strongest
defeats and uses as much information as it can without creating
ambiguity.
 Schulze repeatedly removes the weakest defeat until ambiguity
is removed.
Minimax could be considered as more "blunt" than either of these
approaches, as instead of removing defeats it can be seen as
immediately removing candidates by looking at the strongest defeats
(although their victories are still considered for subsequent
candidate eliminations).
KemenyYoung method
The KemenyYoung method considers every possible sequence of
choices in terms of which choice might be most popular, which
choice might be secondmost popular, and so on down to which choice
might be least popular. Each such sequence is associated with a
Kemeny score that is equal to the sum of the
pairwise
counts that apply to the specified sequence. The sequence with
the highest score is identified as the overall ranking, from most
popular to least popular.
When the pairwise counts are arranged in a matrix in which the
choices appear in sequence from most popular (top and left) to
least popular (bottom and right), the winning Kemeny score equals
the sum of the counts in the upperright, triangular half of the
matrix (shown here in bold on a green background).

... over
Nashville 
... over
Chattanooga 
... over
Knoxville 
... over
Memphis 
Prefer
Nashville ... 
 
68 
68 
58 
Prefer
Chattanooga ... 
32 
 
83 
58 
Prefer
Knoxville ... 
32 
17 
 
58 
Prefer
Memphis ... 
42 
42 
42 
 
In this example, the Kemeny Score of the sequence Nashville >
Chattanooga > Knoxville > Memphis would be 393.
Calculating every Kemeny score requires considerable computation
time in cases that involve more than a few choices. However, fast
calculation methods based on
integer
programming allow a computation time in seconds for cases with
as many as 40 choices.
Ranked Pairs
In the
Ranked Pairs method, pairwise
defeats are ranked (sorted) from strongest to weakest. Then each
pairwise defeat is considered, starting with the strongest defeat.
Defeats are "affirmed" (or "locked in") only if they do not create
a cycle with the defeats already affirmed. Once completed, the
affirmed defeats are followed to determine the winner of the
overall election. In essence, Ranked Pairs treat each majority
preference as evidence that the majority's more preferred
alternative should finish over the majority's less preferred
alternative, the weight of the evidence depending on the size of
the majority.
Schulze method
The
Schulze method resolves votes as
follows:
 At each stage, we proceed as follows:
 # For each pair of undropped candidates X and Y: If there is a
directed path of undropped links from candidate X to candidate Y,
then we write "X → Y"; otherwise we write "not X → Y".
 # For each pair of undropped candidates V and W: If "V → W" and
"not W → V", then candidate W is dropped and all links, that start
or end in candidate W, are dropped.
 # The weakest undropped link is dropped. If several undropped
links tie as weakest, all of them are dropped.
 The procedure ends when all links have been dropped. The
winners are the undropped candidates.
In other words, this procedure repeatedly throws away the weakest
pairwise defeat within the top set, until finally the number of
votes left over produce an unambiguous decision.
Defeat strength
Some pairwise methods—including minimax, Ranked Pairs, and the
Schulze method—resolve circular ambiguities based on the relative
strength of the defeats. There are different ways to measure the
strength of each defeat, and these include considering "winning
votes" and "margins":
 Winning votes: The number of votes on the
winning side of a defeat.
 Margins: The number of votes on the winning
side of the defeat, minus the number of votes on the losing side of
the defeat.
If voters do not rank their preferences for all of the candidates,
these two approaches can yield different results. Consider, for
example, the following election:
45 voters 
11 voters 
15 voters 
29 voters 
1. A 
1. B 
1. B 
1. C 


2. C 
2. B 

The pairwise defeats are as follows:
 B beats A, 55 to 45 (55 winning votes, a margin of 10
votes)
 A beats C, 45 to 44 (45 winning votes, a margin of 1 vote)
 C beats B, 29 to 26 (29 winning votes, a margin of 3
votes)
Using the winning votes definition of defeat strength, the defeat
of B by C is the weakest, and the defeat of A by B is the
strongest. Using the margins definition of defeat strength, the
defeat of C by A is the weakest, and the defeat of A by B is the
strongest.
Using winning votes as the definition of defeat strength, candidate
B would win under minimax, Ranked Pairs and the Schulze method,
but, using margins as the definition of defeat strength, candidate
C would win in the same methods.
If all voters give complete rankings of the candidates, then
winning votes and margins will always produce the same result. The
difference between them can only come into play when some voters
declare equal preferences amongst candidates, as occurs implicitly
if they do not rank all candidates, as in the example above.
The choice between margins and winning votes is the subject of
scholarly debate. Because all Condorcet methods always choose the
Condorcet winner when one exists, the difference between methods
only appears when cyclic ambiguity resolution is required. The
argument for using winning votes follows from this: Because cycle
resolution involves disenfranchising a selection of votes, then the
selection should disenfranchise the fewest possible number of
votes. When margins are used, the difference between the number of
two candidates' votes may be small, but the number of votes may be
very large—or not. Only methods employing winning votes satisfy
Woodall's plurality
criterion.
An argument in favour of using margins is the fact that the result
of a pairwise comparison is decided by the presence of more votes
for one side than the other and thus that it follows naturally to
assess the strength of a comparison by this "surplus" for the
winning side. Otherwise, changing only a few votes from the winner
to the loser could cause a sudden large change from a large score
for one side to a large score for the other. In other words, one
could consider losing votes being in fact disenfranchised when it
comes to ambiguity resolution with winning votes. Also, using
winning votes, a vote containing ties (possibly implicitly in the
case of an incompletely ranked ballot) doesn't have the same effect
as a number of equally weighted votes with total weight equaling
one vote, such that the ties are broken in every possible way (a
violation of
Woodall's symmetriccompletion criterion), as
opposed to margins.
Under winning votes, if two more of the "B" voters decided to vote
"BC", the A>C arm of the cycle would be overturned and
Condorcet would pick C instead of B. This is an example of
"Unburying" or "Later does harm". The margin method would pick C
anyway.
Under the margin method, if three more "BC" voters decided to
"bury" C by just voting "B", the A>C arm of the cycle would be
strengthened and the resolution strategies would end up breaking
the C>B arm and giving the win to B. This is an example of
"Burying". The winning votes method would pick B anyway.
The requirement of singlepeakedness
The Condorcet criteria requires preferences to be singlepeaked; it
is possible to rearrange policies or voting options such that each
individual has a local maxima. The outcome of singlepeakedness is
one in which the median voter is always on the winning side as the
preferences coincide with majority voting in this case.However a
"voting paradox" arises, if preferences are not singlepeaked then
a problem of transitivity arises. This paradox is evidently visible
with an example, where numbers represent preferences such that
1>2>3:

Policy X 
Policy Y 
Policy Z 
Individual A 
1 
2 
3 
Individual B 
3 
1 
2 
Individual C 
2 
3 
1 
If we compare policy X and Y; then X is chosen (Individual A and C
prefer X more than Y compared to B who prefers Y more). Thus, in
accordance to the Condorcet criteria, we compare the "winner"
policy X with policy Z. So policy Z is the chosen policy according
to majority voting in this example.However assume the same voting
procedure was repeated; however this time comparing policy Y and Z
first then pair wise comparisons allow us to conclude that Y will
be chosen and when compared with policy X, then as before X is
chosen. Thus with the same preferences and assuming same voting
conditions two different results arise from majority
voting.Preferences are intransitive.
Related terms
Other terms related to the Condorcet method are:
 Condorcet loser: the candidate who is less
preferred than every other candidate in a pairwise matchup.
 Weak Condorcet winner: a candidate who beats
or ties with every other candidate in a pairwise matchup. There can
be more than one weak Condorcet winner.
 Weak Condorcet loser: a candidate who is
defeated by or ties with every other candidate in a pairwise
matchup. Similarly, there can be more than one weak Condorcet
loser.
Condorcet Ranking Methods
Some Condorcet methods produce not just a single winner, but a
ranking of all candidates from first to last place. A
Condorcet ranking is a list of candidates with the
property that the Condorcet winner (if one exists) comes first and
the Condorcet loser (if one exists) comes last, and this holds
recursively for the candidates ranked between them.
Methods that satisfy this property include:
Comparison with instant runoff and firstpastthepost
(plurality)
Many
instant runoff voting
proponents are attracted to IRV because they believe that if their
first choice does not win, their vote will be given to their second
choice. And if their second choice does not win, their vote will be
given to their third choice, etc. This sounds perfect, except it is
not true for every voter with IRV. If someone voted for a strong
candidate, and their 2nd and 3rd choices are elimated before their
first choice is eliminated, IRV gives their vote to their 4th
choice candidate, not their 2nd choice! In fact, the stronger a
voter's favorite candidate is, the lower their vote is likely to be
transferred if that candidate is eventually eliminated. Their vote
can't help their 2nd or 3rd choice until
possibly after
their 1st choice is eliminated.
Condorcet voting takes all rankings into
account simultaneously.
Plurality voting is simple, and
theoretically provides incentives for voters to compromise for
centrist candidates rather than throw away their votes on
candidates who can't win. Opponents to plurality voting point out
that voters often vote for the lesser of evils because they heard
on the news that those two are the only two with a chance of
winning, not necessarily because those two are the two natural
compromises. This gives the media significant election powers. And
if voters do compromise according to the media, the post election
counts will prove the media right for next time. Condorcet runs
each candidate against the other head to head, so that voters elect
the candidate who would win the most sincere runoffs, instead of
the one they thought they had to vote for.
There are circumstances, as in the examples above, when both
instantrunoff voting and the
'
firstpastthepost'
plurality system will fail to pick the Condorcet winner. In cases
where there is a Condorcet Winner, and where IRV does not choose
it, a majority would by definition prefer the Condorcet Winner to
the IRV winner. Proponents of the Condorcet criterion see it as a
principal issue in selecting an electoral system. They see the
Condorcet criterion as a natural extension of
majority rule. Condorcet methods tend to
encourage the selection of centrist candidates who appeal to the
median voter. Here is an example that is
designed to support IRV at the expense of Condorcet:
499 voters 
3 voters 
498 voters 
1. A 
1. B 
1. C 
2. B 
2. C 
2. B 
3. C 
3. A 
3. A 
B is preferred by a 501499 majority to A, and by a 502498
majority to C. So, according to the Condorcet criterion, B should
win, despite the fact that very few voters rank B in first place.
By contrast, IRV elects C and plurality elects A. The goal of a
ranked voting system is for voters to be able to vote sincerely and
trust the system to protect their intent. Plurality voting forces
voters to do all their tactics before they vote, so that the system
does not need to figure out their intent.
The significance of this scenario, of two parties with strong
support, and the one with weak support being the Condorcet winner,
may be misleading, though, as it is a common mode in plurality
voting systems (see
Duverger's law),
but much less likely to occur in Condorcet or IRV elections, which
unlike Plurality voting, punish candidates who alienate a
significant block of voters.
Here is an example that is designed to support Condorcet at the
expense of IRV:
33 voters 
16 voters 
16 voters 
35 voters 
1. A 
1. B 
1. B 
1. C 
2. B 
2. A 
2. C 
2. B 
3. C 
3. C 
3. A 
3. A 
B would win against either A or C by more than a 65–35 margin in a
oneonone election, but IRV eliminates B first, leaving a contest
between the more "polar" candidates, A and C. Proponents of
plurality voting state that their system is simpler than any other
and more easily understood. All three systems are susceptible to
tactical voting, but the types of
tactics used and the frequency of strategic incentive differ in
each method.
Potential for tactical voting
Like most voting methods, Condorcet methods are vulnerable to
compromising. That is, voters can
help avoid the election of a lesspreferred candidate by
insincerely raising the position of a morepreferred candidate on
their ballot. However, Condorcet methods are only vulnerable to
compromising when there is a majority rule cycle, or when one can
be created.
Many Condorcet methods are vulnerable to
burying. That is, voters can help a
morepreferred candidate by insincerely lowering the position of a
lesspreferred candidate on their ballot.
Example with the
Schulze method:
46 voters 
44 voters 
10 voters 
1. A 
1. B 
1. C 
2. B 
2. A 
2. B 
3. C 
3. C 
3. A 
 B is the sincere Condorcet winner. But since A has the most
votes and almost has a majority, A can win by publicly instructing
A voters to burry B with C (see * below). If B, after hearing the
public instructions, reciprocates by burying A with C, C will be
elected. So B has no recourse to the publicly announced plan:
46 voters 
44 voters 
10 voters 
1. A 
1. B 
1. C 
2. C* 
2. A 
2. B 
3. B* 
3. C 
3. A 
 B beats A by 8 as before, and A beats C by 82 as before,
but now C beats B by 12, forming a Smith set greater than one. Even the Schulze method elects A: The path strength of
A beats B is the lesser of 82 and 12, so 12. The path strength of B
beats A is only 8, which is less than 12, so A wins. B voters are
powerless to do anything about the public announcement by A, and C
voters just smile and hope B reciprocates.
Supporters of Condorcet methods which exhibit this potential
problem could rebut this concern by pointing out that preelection
polls are most necessary with
plurality
voting, and that voters, armed with ranked choice voting, could
lie to preelection pollsters, making it impossible for Candidate A
to know whether or how to bury. It is also nearly impossible to
predict ahead of time how many supporters of A would actually
follow the instructions, and how many would be alienated by such an
obvious attempt to manipulate the system.
33 voters 
16 voters 
16 voters 
35 voters 
1. A 
1. B 
1. B 
1. C 
2. B 
2. A 
2. C 
2. B 
3. C 
3. C 
3. A 
3. A 
 In the above example, if C voters bury B with A, A will be
elected instead of B. Since C voters prefer B to A, only they would
be hurt by attempting the burying. Except for the first example
where one candidate has the most votes and has a near majority, the
Schulze method is very immune to burying.
Evaluation by criteria
Scholars of electoral systems often compare them using
mathematically defined
voting
system criteria. The criteria which Condorcet methods satisfy
vary from one Condorcet method to another. However, the Condorcet
criterion implies the
majority
criterion; the Condorcet criterion is incompatible with
independence of
irrelevant alternatives,
laternoharm, the
participation criterion, and the
consistency criterion.
Use of Condorcet voting
sample ballot for Wikimedia's Board of
Trustees elections
Condorcet
methods are not known to be currently in use in government
elections anywhere in the world, but a Condorcet method known as
Nanson's method was used in city
elections in the U.S. town of
Marquette,
Michigan in the 1920s, and today Condorcet methods are used
by a number of private organizations. Organizations which
currently use some variant of the Condorcet method are:
See also: Use of the Schulze
method
Other Considerations
 Condorcet election results show the win margins for every head
to head runoff. If the Condorcet winner (A) is part of an A beats B
beats C beats A Smith set, supporters of
Candidate C will know that Candidate C would win a recall election if candidate B is somehow
kept off the ballot. If Condorcet voting is used, the rules for
ballot access in recall elections may need to be evaluated to take
the potential motives into consideration.
 If every seat in a legislature is elected by the Condorcet
method, the legislators would all be centrists and might all agree
with each on what laws to pass. Some voters prefer to have
opposites in the legislature so they can't pass laws easily. These
voters might prefer the Condorcet method for electing executive
offices.
 If 10 candidates run for governor in a Condorcet race, ballot
counters may need to count 9+8+7+6+5+4+3+2+1 = 45 head to head
runoffs to find the winner. While this is doable, it might be more
practical to still use ballot access laws or primaries, defeating
some of the original intent of the Condorcet method. Computers can
be used to speed up the counts, though some voters fear computers
can be hacked and used for ballot counting fraud. Another option
would be to allow several independent scanner owners count the
ballots and compare results. Volunteer hand counters could then
spot check various candidates and ranks to make sure they match the
subtotals reported by the scanners.
Further reading
See also
 Condorcet loser
criterion
 Ramon Llull (12321315), who with
the 2001 discovery of his lost manuscripts Ars notandi, Ars
eleccionis, and Alia ars eleccionis, was given credit for
discovering the Borda count and Condorcet criterion (Llull winner)
in the 13th century.
Notes and references
External links