The Possibility of Majority Winners When Politics is Multidimensional

The second in a series of essays on the philosophy of democracy and its implications.

In the previous Common Ground Democracy essay, I discussed why the candidate closest to the median voter is most representative of the whole electorate, and thus is the candidate who should be elected, on the assumption that all voters and candidates can be arrayed along a single left-right dimension of partisanship. This assumption is a reasonable one in many contexts particularly in conditions of intense partisan polarization. When virtually all voters identify themselves, to one degree or another, as on either the blue or red side of the partisan blue-red divide—and do so even when they do not view themselves as a “member” of either political party—it makes sense to consider electoral competition as unidimensional. Some voters or candidates may be more moderate than others, but it is reasonable to view them having a place along the single blue-red, or left-right, dimension.

What about the circumstances in which electoral competition cannot sensibly be reduced to a single dimension?

There have been periods in US history when a significant second dimension of politics has developed cutting across the dominant partisan contestation at the time. For example, in the 1830s electoral competition was defined largely in economic terms between the Whig Party of Henry Clay and the Democratic Party of Andrew Jackson. Tariffs to promote domestic industries, which the Whigs generally supported and the Democrats generally opposed, were a primary subject of debate. There were Whigs in both the North and South, and the same was true of Democrats.

But starting in the 1840s and increasingly into the 1850s, a second dimension of electoral competition developed over slavery.  A series of third parties formed over this separate issue, initially the abolitionist Liberty Party, then the Free Soil Party, and finally the Republican Party. These third parties could not easily be located on the Whig-Democrat axis (although in 1844 the Liberty Party could be seen as more “extreme” than the Whigs in opposition to the expansion of slavery westward, which was the dominant topic of that year’s presidential campaign). Instead, the Free Soil movement could be considered as orthogonal to the prevailing Whig-Democrat divide.

One can argue that something similar has happened at other times in US history. The Progressive movement and specifically the Progressive Party, which emerged in the early years of the twentieth century, can be viewed as opening up a new dimension to the Republican-Democrat contestation that existed at the end of the nineteenth century, rather than occupying a particular spot on the existing Republican-Democrat spectrum.  Likewise, George Wallace’s segregationist third-party run in the presidential election of 1968 was not an effort to offer voters a third position on the conventional left-right dimension of labor-business electoral contestation that dominated American politics after the New Deal, but instead attempted to create a different dimension of electoral contestation on the issue of race relations.

Some political scientists assert that American politics always has a second dimension of electoral contestation. The second dimension often is not as dominant as the primary dimension, but it nevertheless exists and plays a role, or so these scholars contend. The relationship of the primary and second dimensions, with one significantly more pronounced than the other, is sometimes described as if American political competition has “one and a half” dimensions.

However we may wish to think about this assertion by political scientists, it seems important that the philosophy of democracy have a coherent and compelling normative view of how elections should be conducted whenever a significant second dimension of electoral contestation exists. Whether it is rare, frequent, or permanent, the presence of this significant second dimension renders the “median voter” model of democratic representation inapplicable. Simply put, the goal of democracy can’t be to elect the candidate closest to the median voter located on a single left-right dimension when the divergent preferences of voters exist in a two-dimensional context.

So, what to do?

Advocates of proportional representation (PR) argue that that PR systems are better able to handle multi-dimensional electoral preferences. In a PR system, specific parties can form to represent the views of voters who prioritize policies along the second, rather than first, dimension. If the US had adopted a PR system in the early nineteenth century, then presumably the Free Soil Party could have existed in Congress alongside the Whigs and Democrats without ultimately breaking apart the existing two-party conflict between Whigs and Democrats. To be sure, as in any multi-party PR system, coalitions would need to form in order to command a majority of votes for passage of legislation. But an advantage of a PR system is that not every election for a seat in the legislature needs to yield a majority-preferred candidate when there is a three-way split between Whig, Democrat, and Free Soil for the allegiance of voters. Instead, the PR system gives each party a fraction of seats in the legislature proportional to that party’s share of support among voters, and then lets the parties sort out who controls a majority of legislative seats.

As attractive as PR may be, it simply doesn’t work for elections to a single office, like the presidency. Therefore, if we want the president to represent the entirety of the electorate, what do we do if the electoral competition among candidates for the presidency exists along two dimensions of political contestation rather than one? Can we make sense of majority rule, or majority voting, in this context?

We certainly should not give up the idea of majority winners too quickly. Even if electoral competition exists along two dimensions, and thus it is not useful to think of a median voter existing in a single dimension, it may be possible to operate a Convergence Voting system to yield a single candidate whom a majority of voters prefer to each alternative candidate. To illustrate this point, consider the hypothetical possibility that the US had used a Top-3 Convergence Voting system for this year’s presidential election, and suppose that the top three candidates were Donald Trump, Kamala Harris, and Liz Cheney.

The contestation among these three candidates would have been in (at least) two dimensions, one of which would have been fidelity to the rule of law, in contrast to the typical left-right competition. It has been commonplace to observe that Liz Cheney is more conservative than Donald Trump according to the traditional liberal-conservative divide. Yet on the “extra” dimension of fidelity to the rule of law, Harris and Cheney are clearly aligned in essentially the same place in opposition to Trump on the far side of that divide.

Even though this hypothetical campaign would have been two-dimensional, that doesn’t mean there wouldn’t have been a single majority winner using Convergence Voting as the electoral method. We can imagine that Cheney might have won a majority of votes against both Trump and Harris when voters considered her head-to-head against each opponent. Enough Trump voters might have supported Cheney over Harris because these Trump voters preferred Cheney’s views on various traditional blue-red issues (like guns, abortion, taxes, and regulation), even though they disliked Cheney’s anti-Trump stance on the rule-of-law dimension. Likewise, enough Harris voters might have supported Cheney over Trump because of their agreement with Cheney along the rule-of-law dimension even though they disagreed strongly with her on traditional blue-red issues. Whether or not it makes sense to think of a single “median voter” as forming the fulcrum of Cheney’s hypothetical majority coalitions against both Trump and Harris separately, in this case Cheney’s majority victories against each opponent in a Convergence Voting system would still make her majority-preferred compared to each other candidate and thus the candidate most representative of the entire electorate.

(Considering this hypothetical should not be taken to suggest that neither Harris nor Trump could not have won a majority of votes even with Cheney in the race. Rather, it’s possible that a majority of voters would have preferred Harris to either Trump or Cheney when considered head-to-head against each. It’s also possible, although less likely given current polls, that a majority of voters would have preferred Trump to either Harris or Cheney. Despite these possibilities, it also remains true—and this is the key point for our current purposes—that, with Cheney added to the race, both Harris and Trump would remain under 50% in terms of the voters who like each of those candidates best and, therefore, Cheney could have ended up preferred by a majority of voters compared head-to-head against both Harris and Trump. In any event, whichever of the three candidates would have won a majority of voters against each opponent, it would be an example of a majority-preferred candidate in the context of an election in which was conducted in two dimensions.)

Even when electoral competition is two-dimensional, a majority-preferred candidate against each opponent is the most deserving to be elected into office, given the democratic principle of giving equal weight to each voter’s preferences. No other candidate would be more representative of the entire electorate. When only one candidate can be chosen, as in the case of a presidential election, it is fairest for the single winner to be the one whom more voters prefer to each alternative.

However, it is not always the case that one candidate will be majority-preferred against each other opponent. Instead, a second dimension of electoral competition makes it more likely that in a race involving three candidates each would end up majority-preferred against one opponent but not the other. In the next essay in this series, we will consider how the philosophy of democracy should handle this situation.