Condorcet Loser in 2016: Apparently Trump; Condorcet Winner: Not Clinton?

• Author: Richard F. Potthoff,Michael C. Munger
• DOI: 10.1177/1532673X211009499
• Published date: 01 November 2021
• Date: 01 November 2021

https://doi.org/10.1177/1532673X211009499

American Politics Research

2021, Vol. 49(6) 618 –636

© The Author(s) 2021

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DOI: 10.1177/1532673X211009499

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Article

Introduction

Legitimacy, transparency, and accuracy are crucial features

of any social choice process. In selecting chief executives,

where the winner affects the future of the courts, public pol-

icy, and bureaucratic personnel, these three factors are even

more important. But legitimacy is conferred by conformity

with existing rules. Transparency requires that rules are

simple, and cause-and-effect relations are clear. Accuracy

requires some consensus that the “best” candidate was

selected, in effect assuming that there is an underlying

shared ranking of alternatives. In the past five years, many

U.S. citizens (Reinhart, 2020) seem to have developed a

sense that the current process of selecting our executive in

effect exhibits none of the three crucial features we have

listed.

In this paper we offer an assessment of the 2016 U.S.

presidential election,1 as a means of gauging the long-term

stress that our electoral system may be under. There have

already been critiques, both in scholarly forums (e.g.,

Muirhead & Rosenblum, 2019) and in the popular press

(e.g., Beinart, 2016), raising questions about the transpar-

ency and legitimacy of the 2016 result, given the complexity

of the Electoral College and the substantial margin by which

Donald Trump lost the popular vote. The attacks on the

legitimacy of elections and the way votes are counted in the

aftermath of the 2020 election have made a descriptive

understanding of this subject even more urgent.

Our focus is on accuracy, because (1) it is the quality most

plausibly subject to scientific evaluation, and (2) a system

that is perceived as inaccurate is likely to fail on grounds of

legitimacy and transparency as well. The specific criterion

we use to evaluate accuracy is venerable—the Condorcet

principle. Modern social choice theorists often employ the

notion of a Condorcet winner (or Condorcet candidate): a

candidate who would defeat all other candidates in pairwise

elections. If a Condorcet winner exists, there is a determinate

answer to the “which candidate is best?” question, at least in

the view of Condorcet himself.2 The Condorcet principle

simply states that if there is a Condorcet winner in the set of

alternatives, that candidate should be selected. Most theorists

would concur with this.3

In spite of this (near) consensus among experts, recogni-

tion of the value of the Condorcet principle is sorely defi-

cient among opinion leaders, the media establishment, and

non-specialist academicians and educators in evaluating the

Electoral College. The chance that a candidate might lose the

popular vote but still win in the Electoral College has—

deservedly—received much attention. But, we claim that it is

1009499APRXXX10.1177/1532673X211009499American Politics ResearchPottho and Munger

research-article2021

1Duke University, Durham, NC, USA

Corresponding Author:

Michael C. Munger, Department of Political Science and Department of

Economics, Duke University, Gross Hall, Durham, NC 27708-0204, USA.

Email: munger@duke.edu

Condorcet Loser in 2016: Apparently

Trump; Condorcet Winner: Not Clinton?

Richard F. Potthoff1 and Michael C. Munger1

Abstract

Using thermometer score data from the ANES, we show that while there may have been no clear-cut Condorcet winner

among the 2016 US presidential candidates, there appears to have been a Condorcet loser: Donald Trump. Thus the surprise

is that the electorate preferred not only Hillary Clinton, but also the two “minor” candidates, Gary Johnson and Jill Stein, to

Trump. Another surprise is that Johnson may have been the Condorcet winner. A minimal normative standard for evaluating

voting systems is advanced, privileging those systems that select Condorcet winners if one exists, and critiquing systems that

allow the selection of Condorcet losers. A variety of voting mechanisms are evaluated using the 2016 thermometer scores:

Condorcet voting, plurality, Borda, (single winner) Hare, Coombs, range voting, and approval voting. We conclude that the

essential problem with the existing voting procedure—Electoral College runoff of primary winners of two major parties—is

that it (demonstrably) allows the selection of a Condorcet loser.

Keywords

Condorcet winner, elections, social choice, U.S. politics

Potthoff and Munger 619

a mistake to ignore the more normatively and practically

grounded Condorcet principle and its ramifications. We

demonstrate that the current electoral system for American

presidents can, and in 2016 possibly did, select the least-

preferred of a set of four candidates.

To accomplish this, we propose a simple, and (we think)

uncontroversial, extension to the Condorcet principle. Let us

define a Condorcet loser as a candidate who loses, or would

lose, to each other candidate in a two-way match against

each. Then the principle is the mirror of the positive claim

above: If a Condorcet loser exists, no accurate voting aggre-

gation mechanism should select that candidate. The implica-

tion of such an analysis is then that any vote aggregation

procedure that selects a Condorcet-loser candidate is in seri-

ous need of reform.4

To conduct the analysis, we follow Abramson et al.

(1995) and Abramson et al. (2002, pp. 127–128) using the

feeling-thermometer data from the 2016 American National

Election Studies (ANES)5 pre- and post-election surveys.

ANES respondents provide such data by rating each candi-

date from 0° (“Very cold or unfavorable feeling”) to 100°

(“Very warm or favorable feeling”).

Respondents who give candidate X a higher thermometer

rating than Y are presumed to prefer X to Y, and would vote

for X over Y in a (hypothetical) two-way race with only that

pair of candidates on the ballot.6 From these thermometer

scores we are therefore able to construct lists for each voter,

from most-preferred to least-preferred candidates.

Our conclusion is that, among the candidates for whom

we have usable data, Donald Trump was a Condorcet loser.7

This is saying something other than simply that his victory

was the result of a particular configuration of rules and cir-

cumstances. That is not surprising, and is in fact well known

already, since Trump lost the popular vote. What is surpris-

ing is that the election process would select a Condorcet-

loser candidate, a striking signal of deep pathology, and a

new reason to consider reform.

The paper proceeds as follows. Section 2 reviews some

normative considerations for “good” electoral institu-

tions. Section 3 presents the Condorcet results for the 2016

election.8 We use the ANES thermometer data in Section 4

to project (disregarding the Electoral College) how the 2016

election results could have fared under different voting sys-

tems—plurality, Borda, (single-winner) Hare, Coombs,

range voting, and approval voting, in addition to our main

interest, the Condorcet system. Section 5 examines possible

relations of single-peaked preferences to placement of 2016

presidential candidates along a spectrum. In Section 6 we

apply principal component analysis to respondents’ answers

to some ANES policy questions and then consider its rele-

vance to our results. Section 7 points to some auxiliary anal-

yses. Different aspects of thermometer scores receive

consideration in Section 8. Section 9 concludes.

Before proceeding to the analysis, it is useful to issue a

general methodological caveat. A variety of objections

might be raised that the 2016 election was peculiar, and in

particular that the degree of negative partisanship was so

extreme that the particular approach of using the compari-

son of thermometer scores on the ANES for comparative

candidate evaluation is suspect. We consider a number of

such objections in Section 8, and the associated Notes for

Section 8 in the Supplemental Appendix. But there are two

general points that can be usefully raised at the outset. First,

this use of thermometer scores has been used by other schol-

ars in the past, for just this purpose (e.g., as early as Brams

& Merrill, 1994).

Second, there is no reason to think that the effects of nega-

tive partisanship are limited to the way respondents fill out

the ANES. It is certainly true that a large number of (appar-

ent) Trump supporters gave Clinton a 0° rating, and that

(apparent) Clinton supporters gave Trump a 0º rating. But we

contend that it was more, rather than less, likely that this

thermometer evaluation would have carried through to actual

voting intentions, and to voting behavior [in (hypothetical)

two-way races; or, more realistically, with ranked ballots],

precisely because negative partisanship was so intense in

2016. There are good reasons to be skeptical that the relative

magnitudes of thermometer scores predict actual binary vot-

ing intentions perfectly, but there is no reason to believe that

this problem was worse in 2016 than in other years, and we

do go to some lengths to investigate possible issues with this

approach in Section 8.

It is important to note, however, that there may have been

at least two reasons to see the “third-party” candidates in

2016 as unusual. First, while many Americans express a

vague desire for “more choice” or “a third party” in most

elections, that preference has been on the increase since 2013

(Jones, 2021). Consequently, while subjects may express a

preference for third-party candidates, the size of this effect

may be magnified by the generic dissatisfaction with the

choices offered by the two legacy parties.

Second, though Stein and (especially) Johnson had some

visibility and political achievements prior to the election, the

level of well-informed opinions of respondents was likely

less than in previous studies of third-party candidates—as

reflected, perhaps, by high levels of 50° (neutral) thermom-

eter scores for Stein and Johnson and of respondents’ failures

to rate them (which we cover in more detail later). On the

other hand, George Wallace, Ross Perot, and Ralph Nader

(for example) had substantial national reputations, and name

recognition, before the election or were able to use advertis-

ing or (in the case of Perot) debate participation to develop

an independent status as candidates on their own. The empir-

ical effect of this difference is not clear; it is possible that,

particularly for an office as important as president, any ambi-

guity, in respondents’ minds, about Stein and Johnson was a

drawback without which the thermometer scores for them

would have been even higher. But it is also at least possible

that the more “generic third-party” status of Stein and

Johnson was inflated in thermometer scores, and the vote