National Politics, Society

Facultative Voting and the Erosion of the Median Voter Theorem

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by Álvaro Rossi, BA Candidate in Economic and Political Science, Columbia University.  

The year of 2016 has been a challenging one for political economists. From the unexpected results of the Brexit and Peace referendums in Great Britain and Colombia respectively, to the unprecedented election of real estate mogul Donald Trump as President of the United States, the past 11 months have presented some of the most unforeseen political events in the last years. Political economists, charged with developing theories behind voting behavior, were shaken with the collective political choices of 2017.

This is also the case of Rio de Janeiro’s 2016 mayoral elections, which have shown an erosion of the “ideological center” in Rio, as fundamental assumptions in voter theory were debunked in this last election. The two candidates of the second-round elections, Marcello Crivella and Marcelo Freixo, ran under significantly opposing ideological platforms. Crivella had famously pushed forward a social conservative agenda propelled by its evangelical voter base while Freixo had historically been a human rights advocate and a liberal legislation defender, being an advocate, for instance, of the demilitarization of the Federal Police of Rio.

The ascent of these two opposing candidates raises questions about a fundamental political voting theory, the Median Voter Theorem (MVT), which, in summary, states that “a majority rule voting system will select the outcome most preferred by the median voter.”[1] This theory system is based on two key assumptions: first, that there must be a majority rule voting system—namely, Rio de Janeiro’s and Brazil’s system—and second, that voting preferences are ideologically coherent.

The second one can be explained by imagining a one dimensional political spectrum where candidates are plotted based on their ideological agenda. Once plotted, MVT argues that if a person’s first pick is the left-most candidate, its second preferred candidate should be the second left-most candidate, and so on, and similarly, if a person prefers the right-most candidate. Once all preferences are accounted, the median voter’s candidate should be the least disliked and the most voted. MVT can be simplified into this: be the “best of evils” and you will be elected. Though problematic, this last assumption has empirical and logical foundations and ultimately allows political economists to predict voting behavior. It’s not perfect, but it tends to be directionally correct, as evidenced by the declared support of Jandira’s (PCdoB) and Molon’s (REDE) towards Marcelo Freixo, and Bolsonaro’s (PSC) support towards Crivella.

The mayoral election in Rio de Janeiro has challenged this theorem. Indeed, according to MVT, a more centrist candidate would be the preferred choice. Indeed, if Pedro Paulo (PMDB), Índio (PSD), or Osório (PSDB), which all have worked in or have close ties to Eduardo Paes’ municipal administration, were elected, this election would have followed the logic of previous elections which chose Cesar Maia (PFL & DEM), Luis Paulo Conde (PFL), and Eduardo Paes (PMDB), all generally considered centrist candidates and strong proxies of Rio’s median voter preference. This, however, was not the case this year, when Freixo and Crivella — considered to represent the left and right of the median voter — were chosen as the two candidates for the second-round face-off election.

These are obvious oversimplifications and there are several factors that can explain the failure of these candidates, such as the fatiguing of certain parties’ public images due to their involvement in the Lava Jato operation, or Pedro Paulo’s allegations of domestic violence[2]. However, I would argue that there is a factor not being widely considered: the weakening of the obligation to vote.

These mayoral elections have had the highest record of “null” votes (“votos nulos”) and absent votes since 2000. The following table[3] shows the regression of voter turnout in the last 8 years:

Year 2008 2012 2016
“Brancos” (Void) 5% 5% 5.5%
“Nulos” (Null) 7.5% 9% 13%
Absents 18% 20% 24%
Total 30.5% 34% 42.5%

This record of null and absent votes, I would argue, can be contributing to the erosion of the center as the preferred electoral option for cariocas. Indeed, in order for Median Voter Theorem to hold, the assumption of an obligatory mandatory voting also needs to hold; however, as the notion of obligatory voting seems to fade in Rio’s society, so does MVT’s classical applicability to it. As voting becomes increasingly more facultative, a new electoral profile arises every election depending on who actually goes to the ballots. This essentially disables the Median Voter Theorem, as a new median voter will arise every time.

So what would this mean for Rio and Brazil’s politics? The answer, I believe, is in other facultative voting societies, such as the United States. Though a parallel cannot easily be traced between Rio and the United States, their voting behavior seems to have some points of conversion—most notably, the fact that they had the exact same voter turnout in 2016: 58%. This would lead us to believe that Rio’s voting behavior could start to mimic that of a facultative-voting society such as the US.

Indeed, in the US as well as in other facultative voting societies, winning an election is less about “covering one’s bases” or being the “best of evils” and more about how strongly a candidate can make voters feel about his or her ideas, to the extent that it will convince the electorate to actually go to the ballots. This is evidenced, for example, in the recent Clinton-Trump election, where CNN political advisor Tami Luhby stated that lower-than-expected voter turnout of Latino and African-American voters, was “key” to Clinton’s failure to win the elections[4]. If Rio continues to have similar levels of voter turnout, its electorate could start behaving similarly: future elections could be less about the range of a candidate’s identity, and more about its depth. Candidates would therefore not adapt to the historical Median Voter; they would be focused shaping a new Median Voter by influencing which populations actually choose to vote.

There are way too many differences between Rio and US politics, ranging from the electoral college system to the sheer massive difference in voting population, but there remains substantial value in comparing voting behavior in societies where voting is facultative rather than mandatory. As Brazilian voters start to deliberately neglect their voting duties—a trend not only present in Rio but in São Paulo, Salvador, and Belo Horizonte as well with voter-turnout at 62%, 65% and 61%, respectively[5]—the Brazilian political environment will start to resemble one where facultative voting is law.

This newfound direction raises serious implications about election strategies, as it debunks voting behavior theories, such as the MVT, which depend on an obligatory voter foundation. It begs politicians and, more importantly, civilians to pay closer attention to the gap being formed among voting populations and preferences. The polarization of American politics has cast an enormous shadow over the US government and will likely become a driving force in the next four years of policy-making. As it is always preferred to learn from others’ mistakes than from one’s own, it would serve Brazil well to learn from other facultative-voting nation’s negative experiences before it virtually becomes one itself.

Works Cited:

[1] Holcombe, Randall G. (2006). Public Sector Economics, Upper Saddle River: Pearson Prentice Hall, pg 155



[4] Tami Luhby, “How Hillary Clinton lost”, CNN, Nov 9, 2016,