The Impact of Voting Theory on Democratic Choice

The Disadvantage of a Single-Choice System

The famed democratic system of Athens was based off of a simple binary vote. Participants placed their rock in a jar to indicate political preference, and the candidate with the most rocks in his respective jar was declared victor. Although participation was limited to free, white, land-owning men, historians applaud the Athenian voting system as one of the first steps towards an egalitarian political state.  The United States utilizes a similar single-choice system – on Election Day, voters cast ballots to designate a slate of electors to comprise the Electoral College, which then holds a direct vote for President and Vice President.

However, the single-choice system does not necessarily guarantee the fairest outcome. In a scenario with more than two competitors, the existence of a third option can shift the distribution of votes. In the 2000 presidential election in Florida, Al Gore, the Democratic candidate, received 2,912,253 of the total 5,963,110 votes, and George W. Bush, the Republican candidate, received 2,912,790 votes. Independent candidates received the remaining 138,067 votes.1 Because Florida was the final state to report election results, 537 votes effectively determined the outcome of the 2000 presidential election. Consider, however, a scenario in which no independent candidates ran for election – the 97,488 votes received by Ralph Nader, the Green Party candidate, would have most likely gone to Al Gore due to ideological similarities.2 The presence of a third candidate dramatically altered the outcome of the election, even though Ralph Nader received only 1.6% of the total votes.1 Because the single-choice system fails to ensure that the winner of a multiparty election will receive the majority of the votes, the system is particularly susceptible to the effects of a third party’s entrance.

Requiring a candidate to receive the majority instead of a simple plurality of votes can eliminate the “third party effect,” but in cases where the vote is split relatively evenly, a separate system must be devised in order to ensure a fair outcome.

Arrow’s Theorem and the Dilemma of Rank Voting

A rank voting system, which requires voters to rank candidates from most to least preferred, offers a potential resolution to the pitfalls of a single-choice system. However, although rank voting ensures a more comprehensive approach to election processes, counting the ballots becomes significantly more complex. While the single-choice system is singularly the popular choice for the tallying of rank votes, other simpler and more straightforward alternatives exist.

The Alternate Vote system is commonly referred to as a “single runoff vote,” in which the candidate who receives the fewest number of “first choice” votes will be eliminated, and the second choices of ballots who ranked the eliminated candidate first will be counted instead. Because the process repeats until a candidate receives the majority of the votes, the system is best suited for races with large pools of candidates; however, detractors rightly claim that single-runoff voting lacks the straightforward methodology characteristic of single-choice counts.

Condorcet counting methods involve identifying pairs of candidates. In each ballot, the amount of times one candidate in the pair defeats another is counted and tallied. Whoever can defeat every other candidate in a pair-wise race is declared the victor. The result makes intuitive sense and seems “fair;” unfortunately, the Concordet method often fails to produce a comprehensive ranking of candidates, requiring the electorate to default to another counting method.

Bucklin voting counts first-choice votes, then adds second choice votes to the tally, then third choice votes, and so on, until a candidate receives a majority. Similarly, Borda counts assign a point value to each ranking and total the number of points each candidate receives. The candidate with the highest Borda count is then declared the winner.

The complicated and occasionally paradoxical nature of tallying rank votes is best explained by Kenneth Arrow, the mathematician famous for Arrow’s Impossibility Theorem, who claimed that no voting system can accurately determine a victor of an election involving three or more candidates.3 The theorem identifies four necessary criteria for “fairness”: unrestricted domain, the Pareto principle, independence of irrelevant alternatives, and individual utilities (non-dictatorship). Having an unrestricted domain requires that, given a set of individual ranked votes, a voting system must produce a complete and consistent result. The Pareto principle states that if every individual prefers one candidate to another, then the resulting ranking must also reflect this preference. Independence of irrelevant alternatives requires that if the voting pool prefers A to B, then the presence of an alternative, C, should not affect the preference. Non-dictatorship states that no single individual has the capacity to consistently dictate the results. The axioms, or fairness criteria, of Arrow’s Theorem are reasonable and rational; the absence of any single axiom jeopardizes the justness of the voting system. However, using the axioms, Arrow proved that such a system is a mathematical impossibility.4

Arrow’s Theorem provides a mathematical explanation for the apparent inconsistencies intrinsic in rank voting – given a set of ballots, single runoff voting, Concordet counting, Borda counts, and Bucklin voting have the potential to yield distinct outcomes. While rank voting undeniably presents a more comprehensive approach to elections, methods of ballot counting will inevitably be flawed.

The Value of Alternate Voting in the Contemporary System

If the murky and insufficiently decisive outcome of the 2000 presidential election in Florida revealed some inherent flaws in the single-choice system, Arrow’s Theorem highlights a glaring shortcoming of ranked votes – they cannot be counted in a fair and consistent manner. Consequently, one system is not preferential to the other; instead, evaluating the benefits and pitfalls of each in the context of the pre-existing political system in place is necessary.

U.S politics is predominantly bipartisan – using the aforementioned example, 99.8 percent of Florida voters chose either the Democratic or Republican candidate, while only 0.2 percent of voters chose an independent candidate[1]. The dominance of two parties results in a practically binary vote, suggesting that the current system, which solely demands a plurality on a state-by-state basis, adequately represents voter desires. Conversely, the Florida election outcome indicates that reducing analysis of the U.S political landscape to that of a wholly bipartisan system can be a gross oversimplification. Independent parties, however small, possess sufficient political sway to dramatically impact the outcome of an election.

While voters aligned with independent parties remain a significant minority, the influence of independent parties may grow as voters feel increasingly disenfranchised by growing partisanship in national politics. Increasing eminence of a third party necessitates a voting system capable of handling the intricacies of voter preference; however, as Arrow’s theorem suggests, the complexities of ranked voting extend far beyond the ballot.

With the 2012 presidential election forthcoming, American society must question how ballots and counting methods reflect the democratic values of majority rule, and whether or not the adoption of a more complex ranking system could better reflect the public preference. The potential impact of future events will grow as voters continue to voice dissatisfaction with the status quo – if movements such as Occupy Wall Street are any indication, the rise of the vocal and disenfranchised majority will be the deciding factor in the 2012 election, and the voting system must be well-equipped to accommodate such shifts.


  1. 2000 official presidential general election results by state.” Federal Election Commission. Accessed August 5, 2012.
  2. Rosenbaum, David E. “Relax, Nader advises alarmed Democrats, but the 2000 math counsels otherwise.The New York Times. Last modified February 24, 2004.
  3. Arrow, Kenneth. “A difficulty in the concept of social welfare.Journal of Political Economy 58, no. 4. (1950): 328-46.
  4. Hansen P. “Another graphical proof of Arrow’s Theorem.” Journal of Economic Education 33, no. 3 (2002):217.
  5. Image credit (Creative Commons): Hartmann, Daniela. “Global Player.” Flickr. Last modified May 28, 2009.
  6. Image credit (Creative Commons): West, Liz. “VOTE!Flickr. Last modified November 4, 2008.

Emily Wang is a student at The Harker School in San Jose, California. Follow The Triple Helix Online on Twitter and join us on Facebook.