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2.2 a theory of aggregation incentives
One way to think of elections is as a series of coordination problems
(Cox 1999). In most elections, there are fewer seats to be ¬lled than there
are potential candidates who would like to ¬ll them. Coordination refers
to the process by which electoral competitors and voters act together to
limit the number of competitors. Potential competitors can coordinate to
reduce the number of actual competitors (e.g., via candidates with-
drawing from the race or party mergers) and/or voters can coordinate to
limit the number of candidates for which they actually vote. Thanks to
the rich literature in comparative electoral studies, we know a good deal
A Theory of Aggregation Incentives 29

about what shapes coordination within electoral districts where district
magnitude and degree of social heterogeneity are key. However, coor-
dination opportunities do not end at the boundary of an electoral district.
Candidates must decide whether to coordinate with candidates from
other districts to form regional or national parties. The leaders of small
parties or factions must decide whether or not to ally with other groups
or parties. Political entrepreneurs in pursuit of executive of¬ce must
decide to what extent they will pursue a nationwide campaign and
organizational strategy. The scope and size of a country™s party system is
the joint product of both coordination within districts and these deci-
sions about coordination across districts.
Unfortunately, unlike intra-district coordination, we know relatively
little about the factors that shape cross-district coordination or aggre-
gation. What factors aid or impede the incentives and ability of actors to
coordinate across districts? When would actors choose to join a larger
national party over a smaller party and vice versa? To begin with, can-
didates, faction leaders, and entrepreneurs might be driven by a concern
over the potential risks and rewards associated with an aggregation
strategy or its alternatives. If they join with a larger party, they will
increase the joint probability of getting into power, but at the risk of
having to share that power with other actors within the party. For
example, a political entrepreneur who successfully organizes a large
national party may ¬nd his or her power checked by rival factional
leaders from within the party. Intra-party factional con¬‚ict is often a
recipe for party, cabinet, and government instability (Chambers 2003;
Druckman 1996; Laver and Sheplse 1990). On the other hand, if can-
didates or factions decide to go it alone, a candidate as an independent
and the faction as a small party, they trade off greater intra-organization
unity with a smaller (though nonzero) chance of getting into power.3 A
variety of factors might conceivably affect actors™ calculations about the
risks and rewards associated with each of these strategies. These include
¬rst, the size of the prize to be divided among potential copartisans/
faction leaders. The smaller the prize at stake the smaller the share any
one actor is likely to receive, ceteris paribus, and the weaker the incen-
tives to cooperate with others to try and capture that prize. Second, if

3
These two options represent the extremes. Actors can and do choose strategies
between these two extremes by forming mid-sized parties.
Building Party Systems in Developing Democracies
30

combining with other actors to form a large national party does not
signi¬cantly increase the joint probability of capturing the prize of
government “ for example if the largest party does not always capture the
executive of¬ce “ then the expectation of rewards for coordination may
not be enough to outweigh the potential risks.
One reason that politicians from different districts might link
together under a common party label is that they face some task that
requires the help of a large number of legislators (Cox 1997). In other
words, for some political tasks, there are economies of scale “ large
groups are better able to accomplish those tasks than smaller groups. A
group trying to accomplish one of these tasks will seek to induce can-
didates from many different constituencies to link or aggregate within a
larger organization “ in this case a political party. One of these tasks is
gaining control of national-level power and resources “ either as an end
in itself or as a means to pursuing other goals. It stands to reason that
the more substantial the power and resources available at the national
level, the stronger the incentives for coordinating to try and capture that
prize. In addition, aggregation incentives will be shaped by actors™
assessment of the chance of gaining control of national-level power and
resources should they succeed at coordinating to form a large national
party.
In short, whether we think of candidates, faction leaders, and
entrepreneurs as motivated by their calculations of the risks and
rewards of coordination or by a desire to pursue goals that require the
cooperation of multiple actors, two key determinants of aggregation
incentives are the perception of the bene¬ts to such coordination and
the probability that coordinating will enable the party members to
enjoy those bene¬ts.
To ¬‚esh this argument out further, and highlight the nested nature of
the argument, imagine a politician with a power base in one district.
(Let us assume for simplicity that this politician is the head of a regional
party.) The decision he must make is whether to coordinate across
districts (i.e., become part of a large party) or to not do so (i.e., be part
of a small party).4 His decision is based on a comparison of the expected


4
A mid-range option could be to form a pre-electoral coalition with other parties. See
Sona Golder™s recent work for a systematic treatment of the causes and consequences
of pre-electoral coalition formation (2006).
A Theory of Aggregation Incentives 31

utility of being part of a large party and the expected utility of being part
of a small party. Given that cross-district coordination does not offer a
guarantee of becoming the largest party in the legislature, the expected
utility of coordinating is as follows:

EUlarge ¼ p°EPLÞ þ °1ÀpÞ°EP$LÞ À C °1Þ

where p is the probability that cross-district coordination produces the
largest party, and 1Àp is the probability coordination falls short of
producing the largest party, EPL is the expected payoff for being the
largest party, and EP$L is the expected payoff for not being the largest
party. C is the cost of coordinating across districts. These costs might be
the real resources that must be expended for such coordination, or we
might think of the cost as the things our politician must give up to
become part of a larger party (i.e., the opportunity cost of coordina-
tion).5 The relevant comparison is the expected utility of coordination
(EUlarge) versus the expected utility of remaining a small party (EUsmall).
The bigger EUlarge is relative to EUsmall, the stronger the incentives to
coordination across districts will be.
Equation 1, however, begs the question, what shapes our politician™s
expectations of the payoff of being the largest party (EPL)? I argue the
following:

EPL ¼ q°LÞ þ °1 À qÞ°FÞ °2Þ

Where q equals the probability that the largest legislative party also
gains control of the chief executive of¬ce, L is the payoff for becoming
the largest legislative party, and 1Àq(F) is the expected payoff to the
largest party if it fails to capture the executive.
Substituting Equation 2 into 1 we get the following:

EUlarge ¼ p°q°LÞ þ °1ÀqÞ°FÞÞ þ °1ÀpÞ°EP$LÞ À C °3Þ

Equation 3 yields several comparative statics. Our politician™s expected
utility of coordinating to try to form a large party is decreasing in C (the
cost of coordination)6 and EUsmall while increasing in

5
For example, joining a larger party means some loss of control of the party label and
party program and loss of control of overall campaign strategy.
6
In Chapter 3, I will consider some factors that may affect the cost of coordination such
as the number of electoral districts and the level of ethnic heterogeneity.
Building Party Systems in Developing Democracies
32


 The probability that cross-district coordination produces the
largest party (p)
 The payoff if the party is not the largest party (EP$L)
 The probability that the largest legislative party controls the
executive (q)
 The payoff to becoming the largest party (the aggregation payoff)
(L)
 The payoff associated with the largest legislative party not
capturing the executive (F)

This simple formalization suggests several possible hypotheses. For
example, aggregation is likely to be more appealing in countries where
the largest party, in the event of not gaining the chief executive, is at
least assured of gaining other important ministries (such as the ¬nance
ministry) than it would be in countries where this is not assured. In
other words, aggregation is more likely where the rewards are still
substantial for coming in second. Likewise aggregation is likely to be
less appealing in countries where small regional parties anticipate that
they will be needed to form a coalition government (and the expected
utility of remaining small is thus relatively high) than it would be in
countries where small regional parties are unlikely to be needed to
form a coalition.
The focus of this book, however, is on the two hypotheses related to
the expected payoff of becoming the largest party (EPL): namely, that
aggregation incentives increase with (1) the payoff to being the largest
party (the aggregation payoff) and (2) the probability that the largest
legislative will actually capture that payoff.7 Again, together these two
factors yield the expected payoff, or expected utility of being the largest
legislative party. The larger this expected utility, the stronger the
incentives to coordinate across districts, ceteris paribus. I discuss the
factors that affect the size and the probability of capturing the payoff in
detail in the next section. Let me conclude this section, however, with a
brief discussion of one other explanation for the degree aggregation
across and within democracies “ the level of social heterogeneity.

7
Cox discusses some of these factors in his analysis of when district bipartism is
reproduced at the national level in both presidential and parliamentary systems (1997,
189“91).
A Theory of Aggregation Incentives 33

One branch of the literature might ascribe aggregation (or the lack
thereof) to preference heterogeneity across geographic regions. This
heterogeneity often arises from societal cleavages (e.g., ethnicity,
religion, class) and hinders aggregation, especially where cleavage
groups are geographically concentrated (Lipset and Rokkan 1967;
Riker 1982; Kim and Onh 1992; Ordeshook and Shvetsova 1994;
Amorim-Neto and Cox 1997; Cox 1999; Morelli 2001; and Brancati
2003). (In terms of Equation 3, we might think of high levels of social
heterogeneity as raising the costs of cross-district coordination.)
However, by themselves societal cleavages are neither necessary nor
suf¬cient to produce poor aggregation. Countries with similar cleavage
structures can have very different national party systems. For example,
Thailand and Venezuela have very similar levels of ethnic fractionali-
zation yet aggregation in Venezuela is much better than in Thailand (see
Table 1.1).8 Likewise, a country with fewer/less pronounced social
cleavages can have worse aggregation than a very divided country (e.g.,
Ecuador, with less heterogeneity than India, has worse aggregation). In
addition, since cleavage structures change very slowly they usually
cannot adequately account for intra-country variation in aggregation
over time. I argue that the in¬‚uence of social cleavages on cross-district
coordination can be understood in much the same way as their in¬‚uence
on intra-district coordination. Namely, societal cleavages interact with
other (largely institutional) variables to shape the incentives and ability
of candidates to coordinate.9 I turn my attention now to these other
variables, beginning with the payoff for aggregation.


2.2.1 Aggregation Payoff: Concentration of Power and the
Prize of Government

Consistent with existing studies that explicitly consider the issue of
aggregation (Chhibber and Kollman 1998, 2004), I argue that the
degree of political and economic centralization can in¬‚uence aggrega-
tion incentives. The logic of the argument is straightforward. If power is
concentrated at the center, a group wishing to wield that power has an

8
Thailand and Venezuela have a fractionalization score of .43 and .48, respectively, on
Fearon™s ethnic fractionalization measure (Fearon 2003).
9
Speci¬cally, for a given level of social heterogeneity the expected utility of becoming
the largest party should be positively correlated with aggregation.
Building Party Systems in Developing Democracies
34

incentive to induce candidates from multiple districts to participate in a
larger organization to compete for that power (see Cox 1997). Aggre-
gation is positively related to economic and political concentration “
greater concentrations of power lead to stronger cross-district coordi-
nation incentives. However, existing studies focus solely on the distri-
bution of power and resources between the central government and
subnational units “ what I term vertical centralization. Distinct from
these previous studies, I argue that vertical centralization is only one of
two important components of the centralization equation.10 Both
components need to be present to produce a maximal aggregation
payoff. Speci¬cally, aggregation incentives are strongest when (a)
power is concentrated at the national level (vertical centralization) and
(b) power is concentrated within the national government (horizontal
centralization). If either component is absent, the incentives to form
large, nationwide parties will be diminished. In other words, this cen-
tralization equation is interactive in nature “ any one component is not
enough by itself to produce a maximal aggregation payoff.

Vertical Centralization
Those who have previously studied aggregation ¬nd that the extent to
which power and control of resources is in the hands of the central versus
subnational governments to be a key variable that accounts for aggre-
gation (Chhibber and Kollman 1998, 2004; Samuels 1998). In Brazil,
where state governments are extremely powerful vis--vis the national
a
government, aggregation is poor (Samuels 1998). Chhibber and Kollman
¬nd that aggregation has varied along with changes in the national
government™s share of total spending in their four country cases (1998,
2004).11 Where power is concentrated at the national level, voters tend
to privilege national issues and vote for national parties. In contrast,
where subnational governments control substantial resources, voters
tend to vote for regional or subnational parties. Chhibber and Kollman
focus on voters™ incentives and behavior; however, it is not dif¬cult to
imagine a companion story that focuses on the incentives of candidates
and nascent party leaders. Where power is concentrated at the national

10
Another difference between Chhibber and Kollman™s work and this study is that I
focus on the incentives and behavior of candidates and party leaders while Chhibber
and Kollman focus on the incentives and the behavior of voters.

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