The majority vote rule and runoff primaries in the United States

The major parties in the United States use primary elections to select party candidates for general elections. While most employ a simple plurality vote rule for this purpose, some states, primarily southern, employ a majority rule that requires a runoff between the top two vote recipients if no candidate receives a majority in the initial primary. Data on primaries for state Governor and U.S. Senator from 1980 to 2002 are used to examine contemporary concerns about runoffs. Included in the findings are (1) the problem that majority runoffs address – candidates being selected based on low levels of voter support is not a frequent outcome under the plurality rule; (2) the vast majority of selections is based on a majority of votes in a primary, regardless of whether a simple plurality or majority is required; and (3) runoff primaries are necessary in roughly one-third of the contested primaries held in the majority vote context, and in about one-third of them the primary leader loses the runoff.     

Is Rule by Majorities Special?

One way of making decisions is for political associates or their representatives to vote on each issue separately in accordance with the majority principle and then take the cumulative outcomes of such majority decision making to define the collective choice for public policy. We call such a system one of majorities rule. Thought of in spatial terms, majorities rule is equivalent to the principle of making decisions according to the issue-by-issue median of voter preferences. If popular control and political equality are core democratic values, they can be rendered as requirements on a collective choice rule, involving resoluteness, anonymity, strategy-proofness and responsiveness. These requirements entail that the collective decision rule be a percentile method. If we then add a requirement of impartiality, as exhibited in a collective choice rule which would be chosen behind a veil of ignorance, then the issue-by-issue median is uniquely identified as a fair rule. Hence, majorities rule is special. Some objections to this line of reasoning are considered.     

Decision period and Duverger's psychological effect in FPTP elections: Evidence from India

The plurality rule creates incentives that can divert the vote from the third parties. I argue that the process that converts such Duvergerian incentives into the Duvergerian outcomes has a temporal dimension: both strategic and non-strategic voters need time to form and communicate their preferences over candidates. To examine this connection, I capitalize on the institution of phased voting in India. I treat the timing of the district vote as the endpoint of the campaign period in the district and evaluate its effect on the vote for the leaders and the third parties, the third parties’ vote share, and the vote concentration. I find a positive effect of campaign period duration on the extent of the observed strategic behaviors in the district.     

Informational limits to democratic public policy: The jury theorem, yardstick competition, and ignorance

Condorcet’s jury theorem provides a possible explanation for the success of democracies relative to other forms of government. In its modern form, the jury theorem predicts that majority decisions are well informed, because they are based upon far more information than possessed by any single individual. On the other hand, it is evident that democratic politicians and policies are not always as good as the jury theorem implies they should be. This paper uses simulated elections to explore the power and limitations of majority rule as an estimator of candidate quality or policy effectiveness. The simulations demonstrate that slightly informed voters can make very accurate choices among candidates using majority rule. However, as the ratio of slightly informed voters relative to ignorant voters falls, the accuracy of majority decisions declines. The latter implies that institutions, policies, and technologies that promote the dissemination of information also tend to improve the efficiency of democratic governance.     

Proportional Representation,Majoritarian Legislatures,and Coalitional Voting

Voters in elections under plurality rule face relatively straightforward incentives. In proportional representation systems, voters face more complex incentives as electoral outcomes don’t translate as directly into policy outcomes as in plurality rule elections. A common approach is to assume electoral outcomes translate into policy as a vote‐weighted average of all party platforms. However, most of the world’s legislatures are majoritarian institutions, and elections in PR systems are generally followed by a process of coalition formation. Results obtained using this assumption are not robust to the introduction of even minimal forms of majoritarianism. Incentives to engage in strategic voting depend on considerations about the coalitions that may form after the election, and the voters’ equilibrium strategies are shaped by policy balancing and the postelectoral coalition bargaining situation, including considerations about who will be appointed the formateur.     

Inferiority of restricted majority decision rules

The case in which a group of decision makers appoints a committee to choose between two symmetrical alternatives by a simple majority vote, namely restricted majority decision rule, is one member of the set of weighted majority decision rules. It is shown that for any group of decision makers one of the restricted majority decision rules is always the worst of all weighted majority decision rules. This inferiority exists both in terms of the efficiency and in terms of effectiveness of the decision rule. The importance of this finding should be kept in mind when deciding the size of the committee because a seemingly irrelevant change in the number of decision makers may result in the inferior rule, instead of the optimal rule, being used. Moreover, because of the widespread use of restricted majority decision rules and the relatively small number of such rules, the probability of the inferior rule being used is relatively high.     

Gerrymandering Roll Calls in Congress, 1879–2000

We argue that the standard toolbox used in electoral studies to assess the bias and responsiveness of electoral systems can also be used to assess the bias and responsiveness of legislative systems. We consider which items in the toolbox are the most appropriate for use in the legislative setting, then apply them to estimate levels of bias in the U.S. House from 1879 to 2000. Our results indicate a systematic bias in favor of the majority party over this period, with the strongest bias arising during the period of "czar rule" (51st–60th Congresses, 1889–1910) and during the post-packing era (87th–106th Congresses, 1961–2000). This finding is consistent with the majority party possessing a significant advantage, either in "buying" vote options, in setting the agenda, or both.     

Measuring majority power and veto power of voting rules

We study voting rules with respect to how they allow or limit a majority from dominating minorities: whether a voting rule makes a majority powerful and whether minorities can veto the candidates they do not prefer. For a given voting rule, the minimal share of voters that guarantees a victory to one of the majority’s most preferred candidates is the measure of majority power; and the minimal share of voters that allows the minority to veto each of their least preferred candidates is the measure of veto power. We find tight bounds on such minimal shares for voting rules that are popular in the literature and used in real elections. We order the rules according to majority power and veto power. Instant-runoff voting has both the highest majority power and the highest veto power; plurality rule has the lowest. In general, the greater is the majority power of a voting rule, the greater its veto power. The three exceptions are: voting with proportional veto power, Black’s rule and Borda’s rule, which have relatively weak majority power and strong veto power, thus providing minority protection. Our results can shed light on how voting rules provide different incentives for voter participation and candidate nomination.

     

US Presidential Elections: Two Centuries of Constitutional Continuity and Political Change—With an Analysis of the Political Geography of Barack Obama's Re‐election Campaign

The system for electing the President of the United States remains essentially as it was prescribed in the Federal Constitution drafted in 1787. The individual 50 states (plus the District of Columbia) are accorded a number of votes in the (so‐called) Electoral College; each state's Electoral College vote is then attributed to the candidate gaining a plurality (most) of the popular vote in that state; and the candidate with a majority (50% + 1) of these aggregated Electoral College votes is declared the incoming president. What has changed have been the methods of nominating the candidates, chief of which are the political parties from the nineteenth century with their stage‐managed quadrennial conventions and the primary/caucus campaigns from the twentieth century which precede and now determine the formal nomination. President Obama's 2012 re‐election campaign showed both the crucial importance of the much‐maligned Electoral College in winning the presidency and the demographic divisions hidden in the larger American political landscape.     

The Cube Rule in a Mixed Electoral System: Disproportionality in German Bundestag Elections

In the German mixed electoral system the PR tier is generally perceived as fully compensating for any disproportionality in the vote–seat translation generated by the plurality tier. However, as this article shows, the PR tier can itself increase disproportionality. In a mixed electoral system, small parties enter (hopeless) district races with the hope of boosting their PR vote share. But with a high number of district parties, parties may win districts at levels way below the usual 50 per cent vote share threshold. Looking at all 16 Bundestag elections from 1953 to 2009, the article identifies the effective number of district parties as a very strong predictor for the disproportional translation of votes into seats in the plurality tier of Germany's mixed electoral system. The article points to consequences for the internal composition of parliamentary parties, for parties' nomination strategies and for the occurrence of so-called overhang mandates.     

Approval voting,Condorcet's principle,and runoff elections

Approval voting allows each voter to vote for as many candidates as he wishes in an election but not cast more than one vote for each candidate of whom he approves. If there is a strict Condorcet candidate — a candidate who defeats all others in pairwise contests — approval voting is shown to be the only nonranked voting system that is always able to elect the strict Condorcet candidate when voters use sincere admissible strategies. Moreover, if a strict Condorcet candidate must be elected under ordinary plurality voting when voters use admissible strategies, then he must also be elected under approval voting when voters use admissible strategies, but the converse does not hold. The widely used plurality runoff method can also elect a strict Condorcet candidate when voters use admissible strategies on the first ballot, but some of these may have to be insincere to get the strict Condorcet candidate onto the runoff ballot. Furthermore, there is no case in which the strict Condorcet candidate is invariably elected under the plurality runoff method when voters use admissible first-ballot strategies. Thus, approval voting is superior to the plurality runoff method with respect to the Condorcet principle in its ability to elect the strict Condorcet candidate by sincere voting and in its ability to guarantee the election of the strict Condorcet candidate when voters use admissible strategies. In addition, approval voting is more efficient since it requires only one election and is probably less subject to strategic manipulation.     

Voting strength in the European Parliament: The influence of national and of partisan actors

Abstract. Most decisions by the European Parliament are taken by an absolute majority of its members. Some decisions however – such as the approval of the budget of the European Union – require a two-thirds majority. The paper analyzes the a priori voting strength of the member states when their representatives vote coherently. It is shown that the increase in votes for Germany in the 1994 reallocation enhanced its position. A less favourable effect, however, can be seen for the other large members (France, Italy, the United Kingdom, and Spain). However, since votes in the EP tend to be cast according to partisan rather than national affiliation, the relative voting power of the political groups with respect to the two quotas is also analyzed. The tool to measure this is the (normalized) Banzhaf power index, partially extended to account for connected coalitions. The paper demonstrates that the distribution of votes between the present EU member states as allocated in proportion to their population size indeed roughly corresponds to their a priori voting power. However, the relative influence of the largest political groups, the European Socialists and the European People's Party, tends to be overestimated by their share of seats in the framework of the simple majority rule, but it is considerable if the quota is two-thirds. Finally, under the two-thirds majority rule, the European Liberal, Democratic and Reformist Party as well as the small groups appear to be almost powerless. The more the EP gains political leverage – a further increase in its institutional powers is to be expected in the framework of the ongoing Intergovernmental Conference – the more the distribution of voting power between the member states and between the political groups will be a crucial factor in the shaping of EU policies.     

Voting by proxy

I introduce voting by proxy for constructing and operating legislatures, and then compare it to direct representation, plurality, and single transferable vote (STV), which voting by proxy most closely resembles. When each voter uses voting by proxy to select his proxy among given legislators and elections are costless, voting by proxy maximizes the legislature's representation of the voting population. When each voter uses preferential voting by proxy, selecting a proxy during the vote count as well as a proxy in the legislature, and some ancillary rules are followed, I find that voting by proxy dominates STV and offers favorable tradeoffs against plurality. It improves representation and constituent service; eliminates gerrymandering; improves voter turnout; ranks the legislature's representatives by the proxies they hold rather than seniority; creates tighter representative-constituent links that lead to better informed voters, reducing the influence of special interests; and eliminates primary and runoff elections. Extra costs associated with its relative complexity or better representation can be made small.     

Tacit co-operation in three-alternative non-cooperative voting games: A new model of sophisticated behaviour under the plurality procedure

Two models, one due to Farquharson and the other to Niemi-Frank, attempt to account for sophisticated voting behaviour when the voters' preference orderings are common knowledge and communication among Voters is impossible. Having subjected these two models to experimental testing, we have found them lacking. Hence, we propose a new model of sophisticated voting for 3-alternative n-person non-cooperative games under the plurality procedure, which can be extended to other voting procedures and more than three alternatives.The model assumes that voters whose first preference is (one of) the Condorcet winner(s) will (tacitly) co-ordinate their strategies and vote for their first preference, and specifies the conditions under which voters whose second preference is (one of) the Condorcet winner(s) will vote for their second (rather than their first) preference. Consequently, our model predicts that: (i) if there is a single Condorcet winner he or she will be elected; (ii) if there is more than one Condorcet winner the final outcome will be a tie between them; and (iii) when there are cyclical majorities with a single maximin alternative, this alternative will be elected.     

Throwing the rascals out? Problems of accountability in two‐party systems

This article critically examines the concept of ‘accountability’ as it is understood in two‐party systems and majoritarian democracy – namely the ability of voters to remove governments that violate their mandates or otherwise perform poorly. Voters’ capacity to ‘throw the rascals out’ is one of the main normative appeals of two‐partism and the single‐member plurality (SMP) electoral system. However, this article uses a spatial model to show that in at least two types of situation voters are left in a bind when confronted with a mandate‐breaking governing party: (1) when both major parties undertake unexpected non‐centrist shifts in opposing directions after an election, leaving centrist voters with an unappealing choice; and (2) when a governing party that had won an election on a non‐centrist platform undertakes a post‐election shift to the centre, leaving its more radical supporters dissatisfied. In each case, voters have four imperfect options: punish the governing party by throwing the rascals out, but in doing so vote for a party that is ideologically more distant; abstain, and withdraw from the democratic process; vote for a minor party that has no hope of influencing government formation, but which might detach enough votes to allow the ideologically more distant major opposition party to win; and forgive the governing party its mandate‐breaking. All of these options represent accountability failures. The problems are illustrated with two case studies from two‐party systems: the United Kingdom in the mid‐1980s and New Zealand in the period 1984–1993. In both instances, many voters found it difficult to ‘throw the rascals out’ without harming their own interests in the process. The article concludes that accountability may sometimes be better achieved if voters can force a party to share power in coalition with another party in order to ‘keep it honest’ instead of removing it from government completely, as can happen in multi‐party systems based on proportional representation. Thus, although two‐partism based on plurality voting is normally regarded as superior to multi‐partism and proportional representation on the criterion of accountability, in some instances, the reverse can be true. The article therefore undermines a core normative argument advanced by supporters of majoritarian democracy and SMP.     

Manipulability of voting by sincere truncation of preferences

A weak form of strategic voting, called ‘sincere truncation,’ occurs when a voter with a strict preference ranking does not rank all his or her choices on the ballot. A voting procedure is said to be manipulable by sincere truncation if one or more voters can obtain a preferred outcome through sincere truncation. Voting procedures that are not manipulable by sincere truncation are shown to be incompatible with the election of Condorcet (majority) candidates when they exist. A relaxation of simple majority rule, called the ‘7/12 rule,’ is also shown to conflict with nonmanipulability when additional conditions are imposed. These results are formally independent of the strategy-proofness theorems for voting and decision schemes established by Gibbard, Satterthwaite, and others. While their analyses are more inclusive in terms of the varieties of decision procedures allowed, they are also less demanding in their requirements for manipulability since voters are permitted to reverse sincere pReferences in their voting. Thus, plurality voting is manipulable in the sense of Gibbard-Satterthwaite (by preference reversals), but it is clearly nonmanipulable by sincere truncation.     

Plurality versus proportional representation: An analysis of Sicilian elections

The competing merits of plurality and proportional representation have intrigued political economists and political scientists for quite some time. Of primary interest is whether one or the other system is better in serving the interests of the electorate. Since theoreticians are unable to unambiguously determine the answer to this question, the issue must ultimately be decided empirically. We use data from Sicilian elections, where the system was recently altered towards the system of plurality. We are able to demonstrate that the proportional representation system engenders greater information among voters and elicits greater commitment from them than plurality. We are also able to show that in larger towns increased information causes a more dispersed vote under a proportional representation system; further, this result does not hold under plurality. This may have some implications for the size of positional rents reaped by political parties under the two electoral systems.     

The Conditionality of Vote‐Buying Norms: Experimental Evidence from Latin America

Anti‐vote‐buying campaigns led by NGOs and political elites denounce the practice as a crass economic transaction detrimental to democracy. Do potential clients stigmatize vote buying to the same degree, or does the mass public have a more conditional view of the acceptability of vote buying? We theorize that normative evaluations of vote buying vary based on individuals’ understanding of the transaction itself and abstract societal costs associated with the practice. We assess this perspective using survey experiments conducted in several Latin American countries that present hypothetical vote‐buying situations for evaluation by respondents, varying the socioeconomic status of the hypothetical client and the client's political predispositions. We find that the disapproval of vote buying is highly conditional on the attributes of the hypothetical client and that evaluations of vote buying depend on conceptions of the concrete benefits and abstract costs of vote buying as a part of electoral politics.     

An experimental test of the pivotal voter model under plurality and PR elections

This paper examines the decision to vote or not vote in experimental elections. We replicate the important findings of Duffy and Tavits (2008), though with a different design. Our results support their finding, that is, turnout is affected by the belief that one's vote counts and that overestimation in the perception that one's vote counts does not disappear completely over time. Going beyond previous research, we also find that turnout is not higher under a proportional system than under a plurality system, as well as that beliefs about being in a pivotal position have a greater impact on turnout among the risk averse.