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NOV 12 1987
M4 1
Li Sf»A»l«
ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
AN EXPERIMENT
IN
APPROVAL VOTING
Peter C. Fishburn
AT&T
Bell Laboratories,
Murray
Hill,
NJ 07974
John D.C. Little
Sloan School of Management, MIT, Cambridge,
Revised April 1987
WP
MA
U2139
#1782-86
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
AN EXPERIMENT
IN
APPROVAL VOTING
Peter C. Fishburn
AT&T
Bell Laboratories,
Murray
John D.C.
Hill,
NJ 07974
Little
Sloan School of Management, MIT, Cambridge,
Revised April 1987
WP
MA
#1782-86
U2I39
^.t.T.
NOV
UBRARIB
1
2 ^987
RECtWED
ABSTRACT
first major experimental comparison of approval voting with regular
1985 annual election of The Institute of
voting occurred in the
Management Sciences (TIMS). In approval voting a person votes for (approves of)
as many candidates as desired, the winner being the candidate with the most votes.
By permitting more votes than the number of postions to be filled, approval voting
collects more information from the voter than does plurality voting. This can make
In
a difference, for example, when three candidates compete for a single office.
such situations two candidates with wide but similar appeal sometimes split a
majority constituency so that a minority candidate is elected under plurality voting.
Approval voting, by contrast, is likely to identify the candidate who is most broadly
acceptable to the electorate as a whole.
The
plurality
In the TIMS experiment society members received an experimental approval
Two contests involved three
along with their official plurality ballot.
candidates running for a single office and a third, five candidates for two positions.
Surprisingly, in two of the three contests, approval voting would have produced
different winners and neither of the changes was of the type usually emphasized in
the approval voting literature.
ballot
of approval voting and showed
of ballots makes it possible to
is
shown that in each
It
determine why the experimental switches occurred.
reversal the approval winner had broader support in the electorate than the
The experiment also provided empirical data on how voters
plurality winner.
distribute approvals across candidates and indicates that their behavior was roughly,
but not exactly, consistent with theoretical analyses of voting efficacy.
that
it
The experiment demonstrated the feasibility
Direct comparison
can make a difference.
1.
A major experiment
took
during
place
(TIMS)
with
an
annual election of The Institute of Management Sciences
the
plurality
official
examination
compare approval voting with regular plurality voting
Most of the voters
1985.
in
to
INTRODUCTION
of
the
two
filled out
thereby
ballot,
The
methods.
multicandidate elections, which makes
voting
paper
This
date.
to
describes
unexpected phenomena, and shows
permitting
detailed,
a
involved
election
1800
by far the largest field
experiment, analyzes
the
side-by-side
voters
test
its
in
three
of approval
results,
finds
under several quite different circumstances,
that,
winners that have broader electorate support than does
voting provides
approval
it
an experimental approval ballot along
plurality voting.
Approval voting differs from familiar plurality voting by allowing each voter
to vote for
are
any number of candidates.
Each vote
is
a full vote so that, if n
be elected, the n candidates with the most votes win.
to
similar except that each voter votes for at most n candidates.
running for one office,
so both
the
a voter
methods give the same
same
candidates.
office,
under
result.
a
mechanism
to
the
approval
same effect
indicate
is
With two candidates
However, with three candidates running for
voting
Marking one would be similar
would have
Plurality voting
normally marks the ballot for one or the other and
of
one,
two,
or
three
voter
to
ordinary plurality voting, marking two
relative
as not voting,
approval
may mark
a
would indicate approval of two candidates
three
people
all
to
the
third,
and marking
all
although the voter could use such
candidates.
In
such
multicandidate
more candidates beyond the number of positions
elections,
having two or
filled, the
two methods may well produce different outcomes.
to
be
Approval voting may be viewed
as
an
extension
of
plurality
voting that
allows voters to express their preferences more fully in multicandidate elections and
and
provides
so
more
a
The method
candidate.
measurement
complete
was proposed
of
support
electorate
by
independently
people
several
each
for
about
a
decade ago (Ottewell 1977, Kellett and Mott 1977, Weber 1977, Brams and Fishburn
1978,
Morin
then
Since
1980).
has
it
investigators, including Mueller (1979),
(1982),
been
and
explained
Kim and Roush
analyzed
many
by
(1980), Straffin (1980), Riker
Brams and Fishburn (1983) and Merrill and Nagel
(1985).
It
has aroused
controversy (Riker 1982, Arrington and Brenner 1984, Niemi 1984, Nicmi and Bartels
1984,
Brams and Fishburn
1984,
1985) with respect to
party systems and the extent to which
Certain
questions
about
method
elections.
Some
assess
its
is
performance
insight can
might be vulnerable
new method can
Therefore
analysis, but others cannot.
practical
the
is
a
and candidates
in
electorate,
(Majority
and
elections
addressed
relative
existing
to
by theoretical
procedures
the outcomes
in
as a
actual
had approval voting been used (Brams
1984).
Such studies suggest that
superior to existing procedures with respect
lo
fairness to voters
terms of actually reflecting the candidates' support within the
likelihood
the
candidates
pairwise contests.)
to strategic voting.
major concern about approval voting
and Fishburn 1983, Coombs, Cohen and Chamberlin
is
be
possible effects on two-
be obtained by examining data from past elections to
the probable effects on
approval voting
its
are
ones
of
electing
who would
majority
defeat
candidates
all
others
For example, each of the 1970 and 1980
had three main candidates on the
majority candidate, the majority candidates
ballot.
lost
when they
in
exisit.
simple-majority
New York
Senatorial
Although each election had
the plurality elections because
a
some
of
was diverted
support
their
under the votc-for-one
candidates
minority candidates to win.
permitting
thereby
similar
to
If
rule,
had been used, the
approval
majority candidates would have won.
Suggestive
assumptions
how
about
analyses
historical
these
as
arc,
require
invariably
they
would behave under different circumstances from
voters
those actually obtaining and therefore do not provide the same force of evidence or
permit the same depth of analysis that
same
ballots for the
criticism
voting
is
A
that
approval voting
so good, will
out
anyone
is
enabled when voters
to
historical
in
difference ?
a
elections
with more ordinary multicandidatc elections.
how
we can sometimes
voters
By having two
not
only
a
When approval
ballots
Finally,
It
is
from each
overall second choice approval
Is
is
where outcome reversals would
develop
to
a
body of experience
Futhermorc, although
Will
in retrospective
voters
tell
us
multi-choice approval ballot.
voting makes
voter,
a
difference, what causes the change ?
we can observe
generated and
approval voting feasible ?
would be difficult for the voters
(4)
approval
relatively easy to
actual behavior and find out
which candidates are drawing from which others, but
(3)
if
infer preferences, albeit imperfectly, this does not
would actually mark
(2)
implement.
to the
answer the following questions:
almost certainly have occurred, but one would like
studies
two alternative
try it?
Docs approval voting make
extreme examples
in
fill
Nor can retrospective studies respond
too difficult
field test can therefore help
(1)
pick
set of candidates.
is
to
how
it
also
how much
will affect close races.
Some people have suggested
that
it
understand and carry out.
behave
effectively ?
Theory
suggests
that
certain
voting strategies would be most efficacious for the voters, but will they vote this
way
in practice?
The
comparison of approval and plurality voting that we know
field
first
about occurred at the University of Haifa
were
Voters
asked
plurality
ballot
involved.
The
and
submit
to
rank-order the candidates.
experimental
an
Haifa
test
in
worked well
its
with
along
ballot
Only
faculty senate.
its
their
regular
few dozen voters were
a
analyzed in Felsenthal, Maoz and Rapoport (1985), indicate
in the election studied.
The TIMS experiment was on
the
1984 for elections to
to
results,
that approval voting
in
use
of
two
a
far larger scale.
and
ballots
a
It
was patterned
in part
on
However,
ranking of candidates.
unlike the Haifa elections, which had open-ended nominations, only a few candidates
competed for each TIMS office and the number of voters was several orders of
magnitude larger than the number of candidates.
elections to public
and private office
as
is
desirable
and we
shall
to
elect
shall evaluate
the
case
is
much more
like
most people ordinarily think about them.
In discussing the results of the analysis as
it
The TIMS
it
proceeds,
we
shall
assume that
candidates most wanted by the electorate as a whole,
approval voting for
its
do
ability to
that.
In
particular,
assume that majority candidates are good, because they can defeat
candidates in one-on-one runoffs.
In
the
absence of
a
all
we
other
majority candidate other
measures of overall electorate preference will be examined.
We
save to the end of
the paper a wider discussion of criteria for judging voting systems.
The next
section
of
the
paper
summarizes
the
experimental
design
and
provides overall statistics on
the
Subsequent sections analyze the three
balloting.
individual elections and a final one discusses the findings.
Additional supporting
data appear in an appendix.
THE TIMS EXPERIMENT
2.
TIMS by-laws
require that
all
offices be contested and, usually, exactly two
To
candidates are nominated for each position.
might
voting
expected
be
deliberately increased the
one person was
All
of
the
to
number
be elected
candidates
make
to
were
difference,
a
which approval
create elections in
nominating
the
committee
of candidates in three of the elections.
from three candidates;
informed of the
in
the
third,
and agreed
test
to
In two,
two from
five.
participate.
To
preserve a degree of anonymity, the elections will not be identified by office and
the candidates will be designated A, B, C,
.
.
The experiment was announced
.
etc.
the
in
newsletter
society's
1985 and, in April, two ballots were mailed to each member.
ballot
official plurality
determined the binding results of the election and an experimental ballot
assessed
the
effects
We
candidates.
E2
E3
right
of approval
voting in
the
three
races
that
had
at
least
three
shall designate the three elections as:
El
the
An
February
in
an election of one out of three candidates;
another election of one out of three;
an election of two out of five candidates.
In
these elections each voter
of
the
names on
the
was asked
to
check approved candidates
experimental ballot and,
6
in
addition,
to
to
rank the
candidates
(1,
2,
.
.
.)
approval voting, they
might
not
exist
at
assist
there
if
desirable, the experiment
1,851
returned
the
cooperation
by
majority comparisons.
are
ballot.
was designed
This
in
any given
Almost
to
the
all
contest.
Since majority candidates (which
often
are
believed
to
most
be
include this information.
official
Of
ballot.
these,
(85%) also
1,579
remarkably high rate of return shows widespread
members and lends credence
the
arises in the exceptionally small
numbers
majorities)
cyclical
members returned
test
Although rankings are not part of
the left of the names.
number
to
the
results.
of inconsistencies, which run to single digit
(The Appendix provides further
the test ballots
Further support
details.)
had some approvals checked, but
a
few did not
rank the candidates. The counts by response category were:
Rl.
R2.
R3.
Only official ballot returned:
Test ballot also returned, but without rankings:
Test ballot also returned with some rankings:
272
68
1511
(14.7%)
3.7%)
(81.6%)
(
1851
Slightly different
numbers of voters participated
3.
El
was
a
three-way
ELECTION
race
in each election.
El
among candidates
approval voting would have changed the winner from
C
A,
to B.
B,
and
C,
in
As may be seen
which
in
added approval votes for Y = P(Y/A)Na+P(Y/B)Nb+P(Y/C)Nc.
We
from Table
see
1
that
the
does
extrapolation
not
change the results
in
any
fundamental way.
Search for
3.2
we
Next
candidate
rankings.
one
is
candidates.
look
a
majority candidate
for
who would win
The analysis here
Table
is
in
a
As
candidate.
pairwise
little
stated
(plurality)
earlier,
elections
a
with
majority
all
other
more complicated and makes use of the
2 presents the results.
Contest:
A
Inferred votes for:
A
Revealed
majority
a
.
vs.
B
B
A
A
vs.
C
C
B
vs.
C
C
B
first
choices from
official ballot
counts:
166
827
166
835
827
835
166
2
492
290
331
70
66
3
4
9
3
460 1175
900
104
14
13
914
914
Revealed second
choices from:
R3 rankings
R2 approvals
Subtotal of
revealed choices:
334 1322
901
Estimated second
44
choices:
128
89
Extrapolated
total votes:
378 1450**
549 1279**
** larger vote
2.
For election El, majority comparisons show that in hypothetical two-way
races both B and C would defeat A but that B against C would be a virtual tie.
Table
The
essentially
in
listed
C
835 prefer
a
dead
a
that both
The
heat.
with the B versus
illustrated
and are
show
totals
B and C would beat A, but
that
analysis
C comparison.
to B.
However, 166 people
B versus C election? The
to
these
be
will
results
827 voted for B on the official ballot
the first row as preferring
in
leads
B and C are
that
B
to
C (and
show
B
to
A).
How would
cast votes for A.
ballots of these 166
also
Similarly
they vote in
that
70 provided rankings in the order ABC,
66 provided rankings ACB,
3 provided no rankings but approved A and B,
27 made no distinction between B and C by ranking or approvals.
Thus
in
B versus C comparison the 70 are credited
a
and the
3
but gave no indication of a B versus
C
to
B, the 66 to C,
to B.
This leaves 27
preference.
C.
and C
and
if
also
for
A
the 27 are ignored, the revealed choices arc 900 for
If
The next
who voted
to
row of Table
last
2
how
estimates
the 27
would
they adhered to the pattern of the 139 voters (70+66+3)
expressed
27(73/139)=14.2
and
preference
a
for
C
is
nearest vote, are 914 for each.
between
and
B
27(66/139)=12.8.
No
C.
The
B and 901 for
split
who voted
The calculation
final
totals,
between B
B
for
rounded
A
for
to
is
the
valid distinction between the two candidates
is
possible.
3.3
Discussion
.
To summarize, candidate C wins
0.5%, but
the
official
plurality
B would have won an approval vote by 6.1% and
10
a
election
by a hair,
head-to-head election
would be too
is
just
than
a
The picture emerges
close to call.
larger than
little
C (36%
to
23%).
followers do of C.
elect
candidate
to
Approval voting
not
is
when
really
a
the
majority candidate because of an effective
clear
acceptance in the electorate than C.
voters,
is
usually praised because
block
split
case
here.
of
will
would cause the
votes
We do
it
not
have
a
clear
However, approval voting picks
tie.
These show that B has
winner on the basis of second choices.
more information from the
B's
the most approval votes.
candidate
This
lose.
has a loyal following that
Furthermore more of C's followers approve of B than
Hence B wins
majority
a
C
However, among A's followers, more approve of B
B's.
What can we conclude?
often
that
a
broader
a
Therefore, the approval process, by eliciting
leads to the election of the candidate with the
widest support.
We should
possible for
lose
by
the
C
to
also point out that, although
have actually been
approval
voting
a
criterion
approvals to become the winner.
it
did not happen here,
well
as
On
because
B received enough second choice
This could only happen for two close candidates,
the other hand, as seems clear
from various theoretical analyses, approval voting
bring forward majority candidates than plurality voting.
where there
is
"most approval
from the experiment
will
much more
favor of the more broadly supported candidate.
11
as
often
In experimental election El
no clear majority candidate, approval voting demonstrates
to be a tie-breaker in
would be
majority candidate by a few votes and then
but does demonstrate that the criteria of "majority candidate" and
votes" are not identical.
it
its
ability
4.
Election
plurality
E2
and approval
is
another
results agree.
ELECTION E2
three-way
Table
3
race
to
elect
one
presents the results.
person,
but
here
Contest:
A
Inferred votes for:
A
vs.
B
A
B
A
vs.
C
B
C
B
vs.
C
C
Revealed first
choices from
official ballot
counts:
395
552
395
597
552
597
171
281
162
128
3
179
2
240
1
924**
632
91
Revealed second
choices from:
R3 rankings
R2 approvals
1
Subtotal of
Extrapolated
total votes:
620
** larger vote
->**
1
5.
A new
elected
Table
surprise awaits us in election E3, in which two people are to be
from among
winner
in
5
the
shows
ELECTION E3
5
candidates, A, B, C,
official
the
plurality
summary.
pattern as the actual vote and
is
election
(The
D
and
E.
finishes
extrapolated
omitted.)
We
find that the second place
fourth
in
approval
the
vote
approval
voting.
shows the
same
Votes
inferred
Contest for
A
vs
Revealed
first
choices from
rankings
B
Other revealed
choices from
rankings
Revealed choices
from approval
ballots
203
376
25
312
420
22
303
393
21
10
16
12
Totals
550
844*
665
708*
652
673*
398
394
15
10
750*
507
392
234
19
854**
13
513
389
260
22
854**
17
536
537
250
26
420
348
6
15
17
1006**
359
701**
624
535
364
22
9
823**
476
520
375
24
803**
9
487
** larger vote of pair
in
Table 6. Results of hypothetical pairwise contests between the five candidates
E3 show that approval winners B and C would win pairwise contests with all
others.
Figure 1. A graph of the hypothetical pairwise contests within E3 with arrows
toward the winners shows that B, then C, are the two elected. Since there are no
directed cycles, no cyclical majorites are present.
D A
comparisons for E3 are transitive with ranking B C
Rankings from three
E.
types of analysis are:
plurality:
BADGE
approval:
majority:
B C
B C
D A E
D A E.
Thus approval voting has faithfully reproduced
voting has not.
Instead, as already noted, plurality voting elevates the fourth place
majority candidate
to
second place and drops the runner-up
The information on individual
makes
Beyond
it
the majority rankings, but plurality
possible
to
that a cohesive minority has voted for
is
fourth place.
voters provided by the experimental setup
understand what has happened.
However, when the electorate
to
A and
B clearly has wide support.
elected
A
given an opportunity to express
by plurality vote.
removing the two-vote constraint, many more approve of C and
example,
Similarly,
for
23%
20%
A approved
of
those
not
not voting for
voting
D
for
C on
approved of D.
of A.
16
the
official
preferences by
its
ballot
D
than A.
approved of
For
C.
But only 14% of those not voting
E3 with
and two positions
five candidates
its
an at-largc election.
is
Given
freedom of approval voting, the electorate picks C, who has broad acceptance,
the
who
than A,
rather
is
A would
fluke of bland approval, since the rankings show that
head election with C (and even with D).
proposition
may
that
feel
however,
wishes
is
of
a
be
to
separate
the
to
such
elected,
issue
electorate
be
(to
as
a
a
is
in
head-to-
a
this
in
group
up
representation.
By
later).
approval
perhaps believing
situation,
have
should
voting
has
the
Some people
pick majority candidates.
brought
whole,
lose
not a
this
Thus the experiment demonstrates
cohesive group should win
the
two
with
that,
approval voting tends
that
However,
favored by the cohesive minority.
the
criterion
selected
the
This,
of
the
right
candidates.
6.
DISTRIBUTION OF APPROVAL VOTES
One question about approval voting
to
whether
assert
Another question
is
show that votes for
is
these
whether people
either one or
about equally efficacious,
It
i.e.,
instructive therefore to
elections El
would
have
been
people
two candidates
in
a
approval:
approvals:
votes.
have about the same chance of affecting the outcome.
examine the distribution of the number of approvals
E2
720 (55%)
706(49%)
418(32%)
(
approval
three-candidate election are
660 (46%)
69
as
Brams and Fishburn (1983)
and E2:
2 approvals:
3
expressed
will vote effectively.
El
1
will
Restrospective analyses can sometimes infer preferences but are
actually vote for?
unable
how many candidates
is:
5%)
161 (12%)
17
in
We
majority
great
the
that
see
theoretically effective strategies.
of
each.
approvals
More surprising
have
the
is
Less predictably,
the
same effect on
However, three approvals do indicate
individuals
voter as
feature
are
is
to
that in El,
vote
voters
of
for
that
outcome
of
perform the functions of the
where approval voting produces
more double approvals and fewer
triples.
the
of
three,
This
the
election
as
three
since
not
voting.
candidates arc acceptable
the
all
two,
or
we find roughly equal numbers
number who approve
the
one
either
may
office.
a
to
the
Another interesting
reversal of outcome, there
reflect the closeness of
two
of the candidates and the remoteness of the third for most voters.
Brams and Fishburn (1983) further suggest
the distribution of preferences in the electorate,
four or more,
it
is
that,
when
under certain assumptions of
the
number of candidates
efficacious to vote for about half of them.
examine the distributions of approvals for E3,
in
In
this
light
which two candidates are
picked from five:
E3
1
approval:
2 approvals:
3
approvals:
4 approvals:
5 approvals:
Thus most voters appear
to be
116
641
(
8%)
(46%)
494 (36%)
75 ( 5%)
54
(
4%).
using the leverage of approval voting effectively.
18
to
is
we
be
CONCLUSIONS
7.
TIMS experiment
What does
the
Approval
voting
makes
a
say about approval voting as a method?
difference
experimental
the
In
.
outcome would have changed for two of the four positions
obviously has limited scope, the number of reversals
filled.
a
is
little
contests,
the
Although the
test
Most
surprising.
analyzed historical elections have been selected because they contain conspicuous
reversals of
presumed popular sentiment.
Our examples
are
more ordinary, created
make
only to have enough candidates so that the voting method might
The
experimental
data
experimentally found switches
most
of
its
publicity,
that the approval voting
plurality winner.
tie.
Approval
why
us
Interestingly,
.
of the type for
Nevertheless, in
splitting
a
both of our cases
of
the
majority
so
that
a
we can demonstrate
winner has broader support among the electorate than the
In election El, the ranking data
voting
neither
which approval voting has received
two popular candidates
i.e.,
minority candidate wins.
is
tell
a difference.
breaks
the
tie
because
show two candidates
it
preferences, essentially second choice information.
would switch the winner
to
a
majority candidate
collects
more
in a virtual
data
on
voter
In election E3, approval voting
who would win
in
one-on-one
contests with each of the relevant candidates.
Even election E2,
deeper analysis,
a
for
which plurality and approval
results agree, provides,
on
case for the ability of approval voting to identify the candidate
19
Rankings indicate
with the broadest support.
winner would have been virtually
the
election,
runner-up
to
The approval
a
head-to-hcad election, the
who
takes
enough votes away from the
would break the
The population
as
a
the actual plurality
In
This situation leaves one a
election
seems more satisfactory.
in
with the runner-up.
spoiler
a
is
winner.
the
create
about fairness.
that
candidate
third
tied
that,
tie
little
uncomfortable
on a different basis, one
whole gives the winner more
approval votes than the runner-up, the deciding factor being second-choice votes.
Approval voting
Approval voting
society.
schemes operating
in
Most,
in
a
feasible
is,
major
in
but
at least for the
members
fact, operationally simpler
cities
not
all,
voters
three candidate race
two candidates
,
today.
In
of
TIMS,
a
professional
than some of the voting
experiment, no special problems
the
Voter inconsistencies were extremely few.
were encountered.
that,
is
act
effectivelv
for one
.
Theoretical
postion, voting for exactly one or exactly
efficacious and that, in a race with
is
about half offers the most influence
to
arguments suggest
the voter.
many
candidates, voting for
The distribution of numbers of
votes in the experimental elections suggests that most of the voters behave in these
ways.
Somewhat
surprising
is
the
number
of voters
(5%, 12%, and 4%, respectively, in the three races).
meaning that
all
desires of
has
said
Critics
it
This behavior
of
is
all
candidates
interpreted as
the candidates are acceptable to the voter.
The discussion
the
who approve
the
does.
so far has focused on
electorate
whether approval voting better reveals
than plurality voting, and the experimental evidence
However, other questions have been raised about the method.
have suggested that approval voting could be deleterious
20
to
the
two-party
system
and
obviously
that
might
it
on
silent
is
vulnerable
be
the
question
first
beyond
and,
distributions of actual approval votes, seems to offer
A
further concern
Perhaps
not prevail.
a
is
that perhaps in
split
experimental issue but one of criterion.
came up
winners
election
in
A
that the small group
to
C
in
experiment
but
majority.
a
the
In
only
to
more than two
a
same genre
exposes
contest.
the
Again
is
the
The
B and
were
One may argue
chooses C.
a
is
One
phenomenon.
criterion
response
C.
When
group of supporters.
it
that
plurality
representation even though
this
not an
is
situation
offices.
candidates
tight
votes,
take advantage of a
This, of course,
majority
the
who wanted A should have
head-to-head
a
interesting
some cases the majority wishes should
wins the plurality vote because of
the electorate at large can cast
lose
A
rather
on the second.
E3 with the five candidates for two
were candidates B and
Candidate
the
minority candidate should be able
when two popular candidates
situation
little
The experiment
voting.
strategic
to
A would
question.
would
be
The
that
representation can and perhaps should be handled in the design of the election, not
the
voting
geographically
or
representation
groups
can
be
divided
by other relevant segmentation into separate elections.
Within
process.
If
desired,
is
each election the voting process can be made as broadly based as possible.
In
summary,
the
experiment provides direct evidence that approval voting
obtains more information from the voter and uses
the
ranking methods but with much
tabulator.
appears
to
to
capture the central tendency
The approval method does
of the electorate better than plurality voting.
as well as
it
less
this
about
effort on the part of the voter and
Unlike many new or rediscovered voting schemes, approval voting
be an easily understood alternative to the plurality and plurality-with-
21
runoff
now
methods
widely
used
multicandidate
large-electorate
for
Approval voting could therefore save much public and private expense,
time, in those cases
elections.
well as
as
where runoffs are now required.
ACKNOWLEDGEMENT
The authors wish
1985
thank the TIMS Council, the nominees for office
to
the
in
annual election, and, particularly, Dr. H. Newton Garber, chairman of the
nominating committee, for their support
experiment.
We
also
in
authorizing
and
executing
the
TIMS
thank Mary DeMelim and the TIMS Business Office for much
help in designing the ballots and transcribing the votes.
REFERENCES
Arrington, T.
and
S.
Brenner, "Another Look
S.
at
Approval
\'oting,"
Politv
17
.
(1984), 118-134.
Brams,
S.
J.
and
P.
C.
"Approval
Fishburn,
Voting,"
Amcr.
Pol.
Sci.
Rev.
72
.
(1978), 831-847.
,
,
Approval Voting Birkhauscr, Boston, 1983.
.
"A Careful Look
at
'Another Look
at
Approval Voting'," Politv
.
17
(1984), 135-143.
,
Voting',"
Coombs,
C.
H.,
J.
of Strategic Voting under Approval
"Comment on 'The Problem
Amer.
L.
Pol. Sci.
Cohen and
Rev. 79 (1985), 816-818.
.
J.
Chamberlin, "An Empirical Study of Some
Election Systems," Amer. Psychologist
22
.
39 (1984), 140-157.
Felsenthal,
Maoz and
Z.
D.,
Voting
in
A.
Genuine
Rapoport, "Comparing Approval
Elections,"
IPDM
Report
No.
21,
with
Plurality
Laboratory
Information Processing and Decision Making, University of Haifa,
of
Israel,
1985.
Kcllctt,
J.
and K. Mott, "Presidential Primaries: Measuring Popular Choice," Polity
(1977), 528-537.
11
Kim, K. H. and
F.
Roush, Introduction
W.
New
Marcel Dekker,
Merrill,
S.
.
Ill
and
J.
Mathematical Consensus Theory
to
.
York, 1980.
Nagel, "The Effect of Approval Balloting on Strategic Voting
under Alternative Decision Rules." Preprint, Department of Mathematics,
Wilkes College, Wilkes-Barre, PA, 1985.
Morin, R.
A., Structural
New York
Reform: Ballots Vantage.
.
1980.
Mueller, D. C, Public Choice Cambridge University Press, Cambridge, 1979.
.
Niemi, R.
"The Problem of Strategic Voting under Approval Voting," Amer.
G.,
Sci.
Niemi,
R.
Pol.
Rev. 78 (1984), 952-958.
.
and
G.
L.
M.
Bartels,
"The
Responsiveness
of
Approval
Voting
to
Political Circumstances," PS, 17 (1984), 571-577.
Ottewell, G., "The Arithmetic of Voting," In Defense of Variety 4 (1977), 42-44.
.
Riker, W. H., Liberalism against Populism:
Democracy and
the
A
Confrontation between the Theory of
Theory of Social Choice
.
Freeman, San Francisco,
1982.
Straffin, P. D.
Weber, R.
J.,
Jr.,
Topics
in the
Theory of Voting Birkhauser, Boston, 1980.
.
"Comparison of Voting Systems," Preprint, 1977.
23
APPENDIX
We provide
here further data to support and enrich the analyses in the text,
especially for elections El and E3.
Ballot transcription and discrepancies
The TIMS Business Office transcribed
for each voter
ballot
the
two
who returned
A few minor
ballots.
and
both to provide consistency checks and to link
discrepancies arose from transcription.
the official plurality votes in El
(Table
the official ballot votes onto the test
B and C are
for A,
166, 827
The same counts from the transcriptions on
1).
835
respectively
(see
Table
and 835 respectively
167, 826
the test ballots are
plurality
"official
7
For example,
None
vote").
of
the
discrepancies affects our conclusions.
Several
E3 approved of
election
Two
in
candidate ranked lower than one they did not approve
of.
a
the
in
voting.
El voters did not approve of their official ballot choice, yet approved of some
candidate.
other
election,
yet
Nine voters
occurred
inconsistencies
interesting
Seven
voters
18 voters failed to
did
same
the
approve of
in
E2.
the
In
five-candidate
E3
candidate selected on their official ballot
a
approved others not selected on the official
ballot.
Rankings
In election El,
ranked
95%
of the voters
three (1415 of
who ranked one
ballot
E3,
1420 voters ranked the candidates, of
210 ranked their
A few
all
first
In
1484).
test
whom
two choices, 189 ranked
E2
24
more candidates on the
was 88% (1161 of
46 ranked onlv their
three,
voters indicated ties in their rankings.
it
or
and 975
(64"/..)
1313).
first
ranked
In
choice,
all
five.
Approval voting. El
Tabic
7
shows the match-ups between approval votes and official plurality
votes along with other data used to obtain the summaries in Table
who returned
part of the tabic includes 1567 voters
their
official
subset
of
candidates
as
none voted for
a
B,
function
of
who approved
1
each candidate as
the
of
voter's
A and
official
C, 24 voted for
For
choice.
ballot
A on
the official
The
"actual
is
obtained from the totals column in the upper
7
summarizes the number of approval votes for
a
function of the candidate voted for on the official ballot.
next two lines record the test-ballot nonresponders
21,
along with
7.
The middle part of Table
(N^ =
ballot for El
79 voted for C, and two voted for nobody.
approval vote" column in Table
part of Table
test
The upper
and shows the number of voters who approved each possible
ballot
example, of the 105 voters
ballot,
a
1.
Ng
=
134,
Nc
=
111),
and
the
who voted on
total
plutality
The
the official ballot
votes
(counted
from
transcriptions on the test ballots plus the nonresponders totals).
The bottom
section
shows
the
calculation
for
extrapolated
totals.
Approval voting. E2
Table
8
does for election E2 what Table 7 does for El.
25
approval
vote
TABLE
7
Number
of voters approving each possible subset of
candidates, broken out by voter's official choice,
plus various summaries and extrapolations.
Election El
Candidates in
approval set
(R2 + R3)
none
ABC
Total
none
ballots
TABLE
8
Number
of voters approving each possible subset of
candidates, broken out by voter's official choice,
plus various summaries and extrapolations.
Election E2
Candidates in
approval set
(R2+R3)
none
ABC
Voter's choice on official ballot
Total
none
ballots
Approval voting. E3
Table 9 shows the number of voters approving each subset of candidates as
function of the candidate pairs they chose on the official ballot.
ABC
shows
that, of 60 people
the official
voted for
ballot,
C and
who approved
20 voted for
E.
Contrary
A and
C,
instruction on
to
for
the official
but are not reflected in Table
in the official totals
Summaries
of
data
the
in
the
main
table
A and B on
B and C, and one person
ballot,
people voted for only one of the five candidates on that ballot.
counted
For example, row-
of A,B,and C, 23 voted for
16 voted
a
number
a
of
These votes were
9.
are
given
at
the
bottom.
Conditional relative frequencies for approving of a candidate not on the official
ballot
pair can
voted for B and
be
computed from
C on
the
(22%), and 53 approved of
did not vote for
20% who did
main
E
A approved
not vote for
D
the table.
ballot, 29
(21%).
of A,
For example, of the 255 voters
who
approved of A (11%), 57 approved of
As noted
in
23% who did
approved of D.
28
Section
5,
not vote for
14% of
the voters
C approved
of C,
D
who
and
TABLE
9:
Number
of voters approving each subset of candidates, broken out by
Election E3.
voter's choice pair on the official ballot.
Candidates
813
°°'^
i^^SB^rfn
Lib-26-67
3
TOAD DD^ T33 &E3