Measuring Efficiency in the
Presence of Head-to-Head
Competition
Thomas R. Sexton, Ph.D., College of Business, Stony Brook
University
Herbert F. Lewis, Ph.D., Department of Technology and
Society, Stony Brook University
Background
Political campaign finance reform has
received much attention in recent years.
 The Bipartisan Campaign Reform Act of
2002 (McCain-Feingold Act) placed new
limits on who can contribute, and how
much they can contribute, to political
campaigns.
 Campaign managers must pay greater
attention to the efficiency with which
campaign funds are spent.

2
The Traditional DEA Model


The traditional Data Envelopment Analysis
(DEA) model, which measures the relative
efficiency of operational units that consume
multiple inputs to produce multiple outputs,
is not well suited for this challenge.
Fails to incorporate the head-to-head nature
of political campaigns in which a candidate
spends money not only to increase the
number of votes he or she receives but also
to reduce the number of votes that his or
her opponents receive.
3
Head-to-Head Competition

Head-to-head competition is common in sports.
◦ Zak et al. (1979), Mazur (1994), Anderson and Sharp
(1997), Sueyoshi et al. (1999), Lozano et al. (2002),
Haas (2003), Fried et al. (2004), and Cooper et al. (in
press).
◦ However, none of these explicitly incorporates the
head-to-head nature of individual contests.
◦ Sexton and Lewis (2003), and Lewis and Sexton
(2004a, 2004b) apply DEA to baseball and formulate
models in which a team uses its resources both to
score runs and to inhibit their opponents from doing
the same.
◦ However, their models analyze season-long data
rather than individual contests.
4
Our Paper: Political Campaigns
We present a new DEA model that explicitly
incorporates the head-to-head nature of political
campaigns.
 We apply the model to the U.S. Congressional
races in New York State in 2002, 2004, and 2006.

◦ We identify races in which the loser would have won
had he or she been efficient.
◦ We identify incumbents as being particularly wasteful
in their campaign spending.
◦ We explore how campaign efficiency and the
aggregate amount of wasteful spending have evolved
over this period.
5
Earlier Studies

Earlier studies have addressed the topic of
whether spending by an incumbent or a
challenger is more efficient.
◦ Jacobson (1978) and Abramowitz (1988) claim that
spending by a challenger is more efficient and
produces larger gains than does spending by an
incumbent.
◦ Others argue that campaign spending by incumbents
and challengers are both efficient while still others
think that neither incumbent spending nor challenger
spending is efficient (Levitt 1994, Gerber 1998, and
Erikson and Palfrey 2000). See also Palda (1996),
Gerber (2004), Mangee (2002), Palda (2002), Goodliffe
(2004), and Primo (2004).
6
DEA Methodology
Linear programming-based methodology first
introduced by Charnes, Cooper, and Rhodes
(1978).
 DEA is an extreme point method that compares
each producer with only the “best” producers.
 It has been applied in many fields: criminal justice
(Lewin et al. 1982), electricity production (Fare
and Primont 1984 and Norton et al. 2002), public
financing for school bus transportation (Sexton et
al. 1994), retail store management (Anderson
1996), campaign financing (Coates 1999), and
blood centers (Pitocco and Sexton 2005).

7
The DEA Approach





Collection of DMUs, each of which consumes
multiple inputs to produce multiple outputs.
Allows for site characteristics: factors that affect
efficiency but lie beyond control of the DMU.
Establishes the efficient frontier based on the
observed best performance among all DMUs.
Evaluates the efficiency of each DMU relative to
this frontier.
The best producers lie on the efficient frontier
and can be used as a reference set for the
inefficient DMUs that do not lie on the frontier.
8
Campaign DEA Model

Consider an election in which there are nt
candidates competing in period t.
◦ We exclude candidates who are unopposed,
those who spend less than $5000, and those who
receive no votes in the general election.
Let xjt = money spent by Candidate j and x'jt
= total money spent by all of Candidate j’s
opponents combined.
 Let yjt = number of votes cast for Candidate
j and let y'jt = total number of votes cast for
all of Candidate j’s opponents combined.

9
One Candidate
xjt
Candidate j
yjt
x'jt
Candidate j’s
Opponent(s)
y'jt
10
Standardized Spending and Votes
Candidate j
Candidate j’s
Opponent(s)
11
Candidate Status

Define three binary variables:
◦ Let Ijt = 1 if Candidate j is an incumbent, with
Ijt = 0 otherwise.
◦ Let Cjt = 1 if Candidate j is a challenger, with
Cjt = 0 otherwise.
◦ Let Sjt = 1 if Candidate j is running for an
open seat, with Sjt = 0 otherwise.

We consider candidate status to be a site
characteristic.
12
Maximize target’s
vote differential
subject to
Target spends less
money
Target’s opponents
spend more
Target gets more
votes
Target’s opponents
get fewer votes
Variable returns to
scales
Target has same
status
Nonnegativity
13
Target Spending and Votes
14
Three Efficiency Measures

: Own spending

: Own votes

: Opponents’ votes
15
Candidate's Votes Received
Thousands
If All xj Were Equal . . .
1000
900
800
700
600
500
400
300
200
Candidate A
100
0
0
200
400
600
800
1000
Thousands
Opponents' Votes Received
16
Candidate's Votes Received
Thousands
If All xj Were Equal . . .
1000
900
800
Candidate B
700
600
500
400
300
200
100
0
0
200
400
600
800
1000
Thousands
Opponents' Votes Received
17
Candidate's Votes Received
Thousands
If All xj Were Equal . . .
1000
900
800
700
600
500
400
Candidate C
300
200
100
0
0
200
400
600
800
1000
Thousands
Opponents' Votes Received
18
Data



We obtained data on votes received and on
campaign spending from the Federal Election
Commission web site (http://www.fec.gov/).
We chose to analyze the congressional
districts in New York State because they are
designed to each incorporate, as closely as
possible, precisely the same population.
In addition, New York has a large number of
congressional districts (29) and candidates,
which is desirable in any DEA model.
19
Candidates and Races
Two-Way
ThreeYear Candidates
Races
Way Races
2002
40
17
2
2004
46
20
2
2006
32
16
0
All
118
53
4
20
Efficient Candidates
Efficiency Measure
Year Candidates
*
2002
40
2004
46
2006
32
All
118
Own
Spending
23
(57.5%)
31
(67.4%)
25
(78.1%)
79
(66.9%)
P-value = 0.0808 in a chi-square test.
Opponents’
Own Votes
Votes*
18
(45.0%)
23
(50.0%)
17
(53.1%)
58
(49.2%)
10
(25.0%)
19
(41.3%)
16
(50.0%)
45
(38.1%)
21
The Consequences of Inefficiency
In 6 of the 57 races (10.5%), a losing
candidate would have won had he or she
been efficient.
 In each case, the losing candidate’s target
candidate would have been a winner, would
have spent less money than the losing
candidate, and would have faced an
opponent who spent more than the losing
candidate’s opponent did.
 One of the six was a challenger, two were
incumbents, and three were running for an
open seat.

22
Election Outcome Reversals
Actual
Spending
Votes
If Loser Efficient
Spending Votes
1.000
$958,545
80,886
$958,545
49,408
1.000
0.611
$1,399,768
78,465
$739,234
78,465
1.000
1.000
1.000
$1,908,440
156,354 $1,923,967 153,723
Manger (C)
1.000
1.332
0.983
$1,367,904
121,855 $1,367,904 162,280
Higgins (O)
1.000
1.000
1.000
$1,332,162
143,332 $1,332,162 118,792
Naples (O)
0.761
1.000
0.829
$1,581,433
139,558 $1,204,117 139,558
Hall (C)
1.000
1.000
1.000
$1,602,865
100,119 $1,602,865 67,445
Kelly (I)
0.920
1.318
0.674
$2,519,164
95,359
Arcuri (O)
1.000
1.000
1.000
$2,192,558
109,686 $2,192,558 82,485
Meier (O)
1.000
1.021
0.752
$1,586,397
91,504
Kuhl (I)
1.000
1.000
1.000
$1,475,375
106,077 $2,351,018 98,845
Massa (C)
1.000
1.017
0.932
$1,445,525
100,044 $1,445,525 101,725
Year CD Candidate
2002
2004
2004
1
1
27
2006
19
2006
24
2006
29
EX
θy
Ey’
Bishop (O)
1.000
1.000
Grucci (O)
0.528
Bishop (I)
$2,316,985 125,678
$1,586,397 93,397
23
Savings and Vote Increases
Total Spending
Year
*
Total Votes
Candidates
Actual
If All
Efficient
%
Reduction*
Actual
If All
Efficient
%
Increase
2002
40
$20,316,640
$9,546,383
53.0%
2,722,205
3,335,012
22.5%
2004
46
$32,501,954
$23,742,105
27.0%
5,002,315
5,877,840
17.5%
2006
32
$40,392,018
$35,687,382
11.6%
2,799,557
3,119,584
11.4%
All
118
$93,210,612 $68,975,870
26.0%
10,524,077
12,332,437
17.2%
P-value = 0.0366 in Kruskal-Wallis one-way nonparametric ANOVA.
24
Spending and Votes per Candidate
Year
Spending per
Candidate
If All
Actual
Efficient
Votes Received per
Candidate
If All
Actual
Efficient
2002
$507,916
$238,660
68,055
83,375
2004
$706,564
$516,133
108,746
127,779
2006
$1,262,251 $1,115,231
87,486
97,487
All
$789,920 $584,541
89,187
104,512
25
Spending per Vote Received
Spending per Vote Received
Year
*
Actual
If All
%
Efficient Reduction*
2002
$7.46
$2.86
61.7%
2004
$6.50
$4.04
37.8%
2006
$14.43
$11.44
20.7%
All
$8.86
$5.59
36.9%
P-Value = 0.0157 in Kruskal-Wallis one-way nonparametric ANOVA.
26
Incumbents Much Less Likely to be
Efficient Spenders
Ex = 1
Ex < 1
Total
% Ex = 1*
Incumbents
15
37
52
28.8%
Challengers
55
0
55
100.0%
Open Seat
9
2
11
81.8%
All
79
39
118
66.9%
*
P-value < 0.00005 in a chi-square test.
27
Conclusions
About two-thirds of Congressional candidates
in NYS in 2002, 2004, and 2006 spent campaign
funds efficiently.
 However, about half could have received more
votes and more than 60% could have kept more
votes away from their opponents.
 Campaigns spend more, but more efficiently.

◦ Campaign spending per candidate and spending per
vote roughly doubled from 2002 to 2006.
◦ Inefficiency accounted for more than half of campaign
funding in 2002 but only about 10% in 2006.
28
Conclusions


More than 10% of losing candidates would
have won had they been efficient.
Effect of inefficiency is dominated by
incumbency status.
◦ Challengers and candidates running for an open
seat are much more likely to be efficient in their
spending.
◦ Yet incumbents won over 96% of elections.
◦ One possible explanation is that incumbents are
likely to have more money on hand.
◦ Given the limited uses for campaign funds,
incumbents have little choice but to spend the
money on campaign activities.
29