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Cox: Making votes count

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Cox. 1997. Making votes count. Cambridge: Cambridge University Press.

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In Brief

"This is a book about strategic coordination broadly conceived, covering both legislative and executive elections, both strategic entry and strategic voting. It investigates the consequences of strategic coordination and those structural features that determine the nature of the coordination problems that political actors face in differing politics." (4)

See abstract in inside front cover.

MY NOTES (more below):

Ch. 1:

  • Key dependent variables: strategic coordination, strategic entry, strategic voting. "Successful electoral coordination necessarily involves a reduction in the number of competitors; but such a reduction just as necessarily entails a selection of which competitors will survive, and this selection potentially has important policy effects." (5)
  • Three key independent variables for the book: (1) nature of electoral institutions; (2) nature of political actors' preferences; (3) nature of actors' expectations.
  • Electoral systems are systems of exchange, much like the price system is in markets (6-8). "The key to the process by which voter demands are anticipated and fulfilled is the system of expectations." (7)

Ch. 2:

  • DUVERGER's "law": a simple plurality election rule ("the simple-majority single-ballot system") favors a two party system.
  • Duverger's "hypothesis": "The simple-majority system with second ballot [run-off] and proportional representation favors multipartyism." (14)
  • DISTRICT-LEVEL: Duverger wrote that the effect of his "law" was limited to "local bi-partism," yet he then tried to extend the logic to say it would lead to a national two-party system. Cox doesn't agree with the extension, so he will use district-level data. [It is possible that local elections will be two-party, but that national elections will have more parties, b/c some parties may only compete in certain regions.] (28)
  • POST-ENTRY: There's a debate whether to examine Duverger's law as having a pre-entry (deterrent) effect, or a post-entry effect (of making some candidates just be ignored as election day approaches). Cox favors the post-entry view. (29)
  • STRATEGIC VOTING VS. SINCERE VOTING: Sincere voting means voting for the candidate/party you agree most with (Nader). Strategic voting means voting for Gore instead of Nader: of the candidates with a chance at victory, you vote for the one you like. You try to get the most bang for your vote.
  • STRATEGIC VOTING AND ELECTORAL RULES: Strategic voting is more common in simple plurality electoral systems than in PR systems, b/c there are fewer parties. However, there is always a degree of strategic voting. "There is a continuum of systems, ranging from those in which strategic voting imposes a constraining upper bound, to those in which it imposes a rarely-constraining or unconstraining upper bound, on the number of parties." (33)


Ch. 3:

  • lots of detailed description of various kinds of electoral rules.
  • tables showing what kinds of rules each country has
  • the rules determine the level of competition, and affect likelihood of coordination failures by affecting incentives for alliances btw parties
  • the point: it's more than just plurality vs PR: there are other ways of creating ways for small parties to survive (e.g. New York state)

Ch. 4: Strategic voting in single-member single-ballot systems

  • A theoretical model of strategic voting stipulating when voters will vote strategically and why. Shows the limits and assumptions of Duverger's law. The points below all come from the conclusion.
  • DUVERGER's law applies only in specific institutional conditions: a single, exclusive, non-fused candidate vote. In other words, there are many ways to promote multipartism; increasing district magnitude is neither necessary nor sufficient to promote multipartism. Runoffs, nonexclusive votes, and fusion candidacies all make life easier for third parties.
  • Duverger's law is also subject to THEORETICAL LIMITATIONS. (1) Not too many voters have a clear first choice and are indifferent among the other two choices (e.g. not too many Nader supporters are hard core). (2) There can't be a sure winner, because then supporters of minor candidates have no reason to vote strategically. (3) Voters must have only short-term motivations (unlike supporters of Perot, who supported a sure loser to build more support for the future). (4) Beliefs about who the trailing candidates are is common knowledge. And so forth.
  • EMPIRICAL EVIDENCE for bipartism has been at the local level, not the national level. There is no reason to expect local bipartism to exert upward pressure and lead to national bipartism.
  • In addition, it may be more appropriate to look at ELITE expectations more than at individual voters' expectations. By deciding who to fund and support, the elites largely determine which candidates will be perceived by the masses as having a chance.


Ch. 8: Strategic voting, party labels, and entry (see conclusion)

  • Duverger and THE LITERATURE on strategic entry: Because "would-be third party candidates" (pg 170) would realize in advance that they would be the victims of strategic desertion by voters, they will therefore not enter the race.
  • LIMITATIONS of this argument: (1) VIABILITY: It may not be clear at the time that entry decisions are made which candidates will be viable (e.g. it wasn't clear up front whether Kerry or Dean would win the 2004 Dem nomination. If it had been a three-way race against Bush, Dean would not necessarily have withdrawn. (2) POLITICIAN'S GOALS: Duverger assumed politicians had short-term goals. However, some, like Perot, may be willing to lose a couple times in order to win eventually (or to force policy concessions).
  • PARTIES' ROLE, therefore, is as long-term coordination devices. Clear expectations about viability do arise, and they are the product "mostly of electoral history and party labels" (170). Party labels, once established, can deter third-party entry if they have two properties: (1) "conveying a certain number of habitual votes into a candidate's total and (2) certifying the candidacy as 'viable'" (170).
  • Thus, Duverger's prediction works only with this CONDITION: "The entry reduction part of the argument goes through if there is a structured party system in Sartori's sense of the term, but may not if there is not a structured party system" (171).
  • So, what will be the minimal viable SIZE of a party? There is an upper bound (which may not be reached) on the viable number of party labels, depending on institutions. This upper bound follows the M+1 RULE. M varies according to three electoral systems, as discussed in part II: "plurality rule in M-seat districts, PR in M-seat districts, and top-M runoffs" (171).
  • When will political aspirants seek to form a NEW PARTY? "The more valuable [it] is [to run] with a major-party label rather than without, and the more permeable ... the major party's nomination process [is], the more likely ... new groups or would-be candidates [are] to "infiltrate" the major party, rather than start a new party, in accord with the old adage: If you can't beat them, join them" (172). Note that there are two variables here: (1) permeability of the old party (how easy it is to join them and change them) and (2) whether you get bigger returns by joining them.


Ch. 10: Putting constituencies together (e.g. the flawed "link" Duverger makes from a theory about districts to a conclusion about national politics)

  • Duverger, Sartori, and others propose a link between Duverger's district-level law and national party structures. Duverger wrote, "Plurality election rules at the district level tend to produce national bipartism" (201). But this argument is WRONG.
  • Duverger's Law is only true nationally if "all candidates find it necessary to join a party that runs candidates in all districts" (201), but there is no reason to ASSUME that this is true. Some parties may run candidates only locally. "Thus, the systemic version of Duverger's Law is incomplete as a theoretical proposition, whatever its merits as an empirical generalization" (201).
  • Whether politics on the national level is bipartisan or multipartisan DEPENDS BOTH ON DISTRICT-LEVEL AND NATIONAL-LEVEL (EXECUTIVE) ELECTORAL RULES.
  • Thus, a revision of Duverer's law: "If a system (1) elects legislators by plurality rule in single-member districts; (2) elects its chief executive by something like nationwide pluarality rule; and (3) holds executive and legislative elections concurrently, then it will tend to" have at most two viable candidates at both local and national levels, and thus a national two- or one-party dominant system (201).
  • REPRESENTATIVE VS EFFICIENT voting also matters: if voters vote efficiently, then strategic voting will arise only in favor of nationally competitive parties.
  • FIVE REASONS why politicians from different districts might want to form a national label. (1) pursuing national policy; (2) pursuing the presidency; (3) pursuing the premiership; (4) pursuing the upper tier seats; (5) pursuing campaign finance.
  • THREE TYPES of portfolio-maximizing strategic voting: (1) Strategic sequencing (controlling parliament to get into coalition); (2) Strategic balancing (of Senate, House, and Presidency); (3) threshold insurance (preventing a prospective coalition partner from falling below the electoral threshold)
  • IN SUM: coordination at the local level affects the number of parties within each district, coordination at the national level affects the degree to which the local party systems cumulate into a national party system (203). The electoral systems in place at both district and national levels interact to determine the national party structure.

Ch. 11: Electoral institutions, cleavage structures, and the number of parties

  • "A cross-sectional MODEL of the effective number of parties (at the national level) in 54 polities" (204)
  • THREE GOALS of the model: (1) to investigate the "hypothesized interaction between social and electoral structure"; (2) to investigate chapter 10's claim that the number of national parties depends interactively on (a) "the degree of integration of executive and legislative elections" and (b) the "strength of the executive choice procedure"; and (3) to "assess the importance of [chapter 10's other national-level variable] the existence of upper tiers" (204).
  • Regarding goal 2, a hypothesized TWO-STEP PROCESS: (1) "Presidential rules combine interactively with social diversity to produce an effective number of presidential candidates' (2) the effective number of presidential candidates affects the effective number of legislative competitors, with the size of the impact depending on the proximity of the presidential and legislative elections" (204).
  • IN SUM: an econometric model that predicts the "effective number of parties at the national level based on variables drawn from both the distric and national levels, and from both institutional and sociological perspectives" (220). Key VARIABLES: district magnitude, social diversity, electoral permissiveness, executive choice procudure, upper tiers, social cleavages (221).
  • GENERAL CONCLUSION: Multipartism is the joint product of both (a) "many exploitable [social] cleavages" and (b) a "permissive electoral system." In other words, the electoral system sets an upper limit on the possible number of parties (the system's "permissiveness"), but bipartism may still result if there aren't enough social cleavages to need more parties.


Ch. 12: Coordination failures and representation

  • Key question: "How will democratic performance be affected when the electoral system broadly conceived (including both the legislative and executive election procedures) becomes stronger?" (An electoral system is stronger if it exerts a stronger incentive for parties to consolidate; i.e. A is "stronger" than B if A has a lower upper bound on the viable number of competitors than B does). (225)
  • LITERATURE's answer: a trade-off between REPRESENTATION VS STABILITY (225)
  • "Representation" = one is represented if one's views are "reflected in the final product ..., enacted policy." Thus:
  • KEY QUESTION: "What kinds of electoral systems, under what conditions, reliably produce centrist outcomes?" (226)
  • THE POINT: "If representation is defined in terms of whether each votere can find a legislator who advocates similar views, then larger district magnitudes obviously enhance representation. If representation is defined in terms of how close the government's policy is to each voter's ideal, then the case in favor of larger-magnitude districts is less immediate and depends crucially on how one thinks the politics of coordination will play out" (236).
  • In a DUVERGERIAN WORLD, then the strongest system (single-member, single-ballot) would lead to two national parties offering similar centrist policies --> stronger = more representative (237)
  • When NON-DUVERGERIAN results crop up, a stronger system can lead to poor coordination by the center, allowing extremists to win in the constituencies and pull national policy far from the median (237)
  • ASSUMPTIONS ABOUT COORDINATION ARE KEY: "If coordination is more likely to fail at the electoral stage, then stronger systems will be more erratic. If coordination is more likely to fail at the government formation stage, then feebler systems will be more erratic" (237).


Ch. 15: Conclusion

  • VOTES DON'T COUNT when people cannot coordinate on a candidate or party. (e.g. those voting for Gore and Nader didn't get their votes counted because they failed to coordinate even though they commanded a majority.)
  • Thus, BETTER COORDINATION by Republicans --> BETTER REPRESENTATION in the White House
  • STRENGTH: "The procedures use to choose who wins spots, seats, and portfolios can be more or less strong -- and the stronger they are, the bigger the coordination problems that political actors face at that stage" (270).
  • STRATEGIC VOTING: Two key assumptions. (1) Short-term instrumental rationality and (2) rational expectations ("i.e., expectations that are consistent with rational behavior on the part of all voters") (271). This article reviews two forms: (1) "seat-maximizing" and (2) "portfolio-maximizing" (272).
  • M+1 RULE: "Typically, no more than M+1 candidates can be viable in SMSP or top-M runoff elections; and no more than M+1 lists can be viable in PR candidates" (271). (M = district magnitude in SMSP and PR, and the number of candidates that advance in runoff elections).
  • FORMAL ANALYSIS has advantages: (1) clearly stated assumptions; (2) clearer statement of conclusions
  • ADVANTAGES OF THIS MODEL OF STRATEGIC VOTING: (1) "Recognizing that the direct effect of strategic cordination falls on electoral competitors -- that is, candidates or lists -- rather than on parties, helps clarify our understanding of systems that allow joint lists or fusion candidacies. In these systems, the number of viable parties may well exceed the number of viable lists or candidates, because more than one party can support a given competitor." (2) "Recognizing that strategic voting only imposes an upper bound on the number of competitors, rather than establishing an equilibrium number, helps to clarify a classic debate about the 'multiplying power' of PR." (3) "Recognizing that strategic voting only imposes an upper bound also changes how one thinks about the relation between electoral and social structure." (273-4)
  • SYSTEMIC COORDINATION: Duverger/Sartori took argued that a district-level theory could explain coordination across districts, leading to a national party system. However, there is one "(well-understood) logic that drives local results. There is another (little-explored) logic that drives cross-district alliance formation" (275).
  • COORDINATION FAILURES also affect the quality of policy.


Cox, Making Votes Count (1997)

Chapter 1: Introduction

The book is concerned with strategic coordination (both strategic entry and strategic voting) in electoral systems. Following Duverger, successful coordination will reduce the number of electoral competitors.

Main IVs are: electoral institutions, political motivations and public expectations. Institutions mostly define the electoral coordination game.

The analogy for electoral systems is the market: a hypothetical equilibrium exists with market clearing expectations which equate the demand of citizens and the supply of candidates. Main point of book is to "explain how different electoral laws affect the nature of market-clearing expectations and electoral coordination" (8).

Chapter 2: Duverger's Propositions

Duverger's Law: simple plurality rule favors a two-party system. Duverger's Hypothesis: simple plurality with second ballot and proportional representation favors multipartyism.

Critiques against Duverger and the institutionalist approach: 1) causal arrow is wrong and party systems actually determine electoral systems 2) from the political sociologists: party systems determined by number and type of social cleavages in society. Cox hopes to synthesize both sociological and institutionalist approaches.

Against the sociological approach, Cox shows that different electoral systems do produce different party systems even within the same country at the same time (between elected upper and lower houses). Important question as to whether Duverger's Law applies to country-wide or district-level elections (Cox deals with district level) and whether applies to pre-entry or post-entry politics (Cox deals with post-entry).

Voters will vote for either one of two candidates because of 1) strategic voting (don't waste vote on unlikely winner) or because 2) political elites only invest resources in serious candidates. Cox believes both explanations are important.

Chapter 3: Electoral Systems

Electoral system is a set of laws and party rules that regulate electoral competition between and within parties (38). Chapter includes lots of terminology on types of voting and districts. Electoral formulas are how votes are translated into seats, and are divided into two main camps: plurality/majority rules and proportional representation. Plurality rules tend to lead towards a majority party in the legislature, while PR leads to more proportional results.

Chapter 4: Strategic Voting in Single-Member Single-Ballot Districts

Duvergerian equilibria: level of strategic voting undercuts support for all but two candidates. Non-Duvergerian equilibria: two or more candidates tied for second, so neither is discounted and more than two significant candidates are left in the field. Duverger law assumes trailing third candidates are reduced to hard core support, all voters are short-term instrumentally rational, identity of front runners and trailers is known. With these assumptions, the model has severe limits.

Chapter 8: Strategic Voting, Party Labels and Entry

Duverger predicts that strategic voting will keep non-viable third-party candidates out of race (strategic entry). Cox adds two restrictions to this: 1) restriction of viability must be clear (or else lots of candidates would enter) and 2) politicians' goals must only concern winning current election. Party labels help a party's candidates and deter non-party candidates from seeking that party's votes (parties serve as coordination mechanisms).

Ch. 10: Linkages between the district and the national level.

The basic question is whether or not single member districts (SMD) encourage the emergence of two parties at the national level. Cox finds that there is nothing in the logic of district-level electoral structure that allows one to conclude that there will be two parties nationally. There may be factors that push toward national bipartism, but these do not depend on district-level electoral structure.

The motivation to form linkages across districts comes from the economies of scale that are necessary to become the president or prime minister. National candidates need support from all over the country, and have a clear incentive to form with legislators in building support. Four factors affect how strong the incentives toward national bi-partisanism will be: 1. strength of the presidency (concentrated vs. divided); 2. strength of the presidential election procedure in presidential systems / strength of the prime minister election procedure in parliamentary systems; 3. executive-legislative electoral linkages; and 4. strength of the legislative electoral system. These variables determine whether SMDs will encourage convergence on two national parties.

The emergence of national parties changes the calculations of strategic voters, who now may use their votes not only to affect the outcome of the district election but also to affect the outcome of national issue (e.g., who will control the national government). When voters engage in nationally-oriented strategic voting, different voting behaviors may occur. Three examples are given:

1.strategic sequencing: voting in order to affect which party gets the first opportunity to form a government.

2.strategic balancing: voting so as to deny a single party control of all branches of government.

3.threshold voting: voting so as to keep a prospective coalition partner's vote above some threshold mandated by the electoral code.

Chs. 12-14: Coordination Failures

These chapters explore how coordination failures affect various aspects of democratic performance.

Representation: If coordination works, strengthening the electoral rules (reducing the number of seats per district) limits the degree of extremism possible / encourages centrism. When voters fail to coordinate, strengthening increases the degree of extremism possible. [Here representation is maximized by centrist policies because they reduce the aggregate distance between each voter's ideal policy point and the actual policy point.]

Dominant Parties: Dominant parties are likely to occur when the ins are better at coordinating than the outs. An example is India where the centrist party gained power. The other parties where arrayed to the left and right of the centrist party, and found it difficult to coordinate with each other.

More generally: some electoral systems create more difficult coordination problems than others. The more difficult the coordination problems are, the more factors other than voters' preferences will matter in determining who gets seats.

Realignment: Realignment can be thought of as a huge coordination game. Realignment is less likely in strong (low number of seats per district) electoral systems because costs of failure are very high. But when realignment does happen, it is more consequential (because only really important issues are big enough to force realignment).

Ch. 15: Conclusion

Vote wasting: Voters that fail to coordinate waste their votes in several ways. One way is voting for a party that has no chance of winning. Another is voting for a party that is guaranteed to win. In order to make votes count, coordination is required.

Upper bound: Typically no more than M+1 candidates can be viable in SMSP or top-M run-off elections; and no more than M+1 lists can be viable in PR elections. The M+1 rule does not specify how many candidates/lists/parties there will be; it merely suggests an upper bound. When the upper bound is exceeded, there will be an incentive for voters to coordinate in reducing the number so as not to waste votes. However, this assumes that voters are instrumentally rational (care about who wins seats in their district at the present time) and voters possess rational expectations (can identify which ones are viable).

Linkages: The number of legislative parties at the national level is best thought of as a joint product of legislative and executive electoral rules, both interacting with social cleavages.