The chaos in the GOP reveals the flaw in democracy we don't usually see

The chaos in the Republican Party produced by the nomination of an unconventional, untested candidate has prompted many to suggest that the party is dying. But much like Mark Twain, the rumors of its death are greatly exaggerated. What we're observing now in the Republican Party is a natural byproduct of democratic systems, but we don't typically see this part of democracy.

In truth, all democratic systems are prone to chaos. The reason we generally experience a certain amount of order in our government is because our system places severe restrictions on our choices.

When most people hear the word "democracy," they think about a system that enacts the will of the people. In our democracy, we tend to use majority rule elections to determine what the people want, and we expect government to enact whatever that is.

We expect our political parties, for example, to nominate candidates that reflect the majority preference of the members of the party. We anticipate that the voting system we use will help us identify this majority preference.

The myth is that more often than not, the "will of the people" does not exist. I'm not just being cynical. The Marquis de Condorcet, a French philosopher and mathematician in the 18th century, proved that under certain circumstances, there is no majority will.

Consider the following hypothetical example. Suppose we think of the Republican Party as being made of three coalitions (libertarians, social conservatives, nationalists), any two of which form a majority. Further suppose these coalitions are trying to determine the party's preference on immigration issues. Their choices are to deport current immigrants who are deemed threatening (Deport), enact security measures to keep new immigrants out (Wall), or strictly limit new immigrants and refugees (Limits). We can represent the rank order of each coalition's preferences like this.

In this example, if the coalitions hold a vote among all these options, we'll have a three-way tie. In order to force an outcome, they might use a two-stage voting system where they only vote on two items at a time. Say, first Wall versus Limits, and then the winner of that versus Deport.

We call the order of the vote the agenda. We can see that in this case, each possible agenda produces a different result.

What we observe is that this group lacks a will, or majority preference. In fact, there is a different majority that prefers each outcome. A coalition of libertarians and nationalists prefer Wall to Limits; a coalition of conservatives and nationalists prefer Deport to Wall; a coalition of libertarians and conservatives prefer Limits to Deport.

The hypothetical party above has no majority will. It is impossible to design a democratic system that finds the group's preference, because the group has no preference (see Arrow's theorem). More accurately, there is a different majority that prefers each outcome.

We call this a majority rule cycle, or a preference cycle. Further, we know that as the number of voters and the number of alternatives increases, the mathematical probability that we will observe a cycle of this type increases.

In reality, it's highly likely that as a society we frequently have cyclical preferences in political and policy choices before us. However, we are not usually aware that we lack a compelling consensus because, by design, we've created institutions that prevent us from revealing these instabilities. If you think the current Congress is inefficient, imagine one that constantly cycled through votes and allowed different majorities to adopt conflicting versions of a bill.

It may appear that our democratic institutions allow us to arbitrarily choose particular majorities over others. Perhaps. But in the absence of some mechanisms that limit our choices and force stability, we would frequently observe chaos.

We use basic democratic institutions to limit our ability to reveal preference cycles. For example, legislative committees and parties place limits on the legislation that Congress considers; the system of primaries limits our candidate choices in elections; the agenda-setting powers of the speaker of the House and majority leader in the Senate force a particular order of voting on alternatives; and so forth.

I don't mean to suggest that all majoritarian outcomes are arbitrary. Sometimes voters are unanimous, or strongly in favor of one alternative over another. Preference cycles, like the stylized example above, only happen some of the time. But we often don't know when they exist because our institutions prevent us from knowing whether a different majority would have chosen a different outcome.

The fissures we see in the Republican Party right now are an example of the type of preference cycles that political scientists know are common but that we don't typically observe. There may be one majority of Republicans who prefer Trump to alternatives, but there may exist other majorities that prefer other candidates. Our selection process didn't reveal those outcomes, so we can't be sure.

There may be a faction of Republicans who prefer strongly nationalist and isolationist policies toward immigration, security, and trade, but there may be a different majority coalition of Republicans who hold different preferences.

The chaos in the Republican Party we now observe is a natural byproduct of competing majorities. At this late stage in the game, the party lacks an institutional mechanism that would force stability, or coordination, in the party over its nominee. The party failed to coordinate on a candidate that might provide the appearance of a stable majority.

Democracy can only enact the "will of the people" if the will exists. What we're seeing from Republicans is a classic preference cycle. There is no single majority preference among the members of the party; rather, there are different majorities that prefer different outcomes. At this late stage in the presidential campaign, we lack institutions that limit our ability to observe different majorities, and the result is chaos.

My argument is that the chaos is almost certainly there much of the time, in many policy and political decisions; we just don't have the luxury of knowing that we lack a majority will because our decision-making process doesn't reveal it. In this year's presidential election, it's been revealed among Republicans.

The Republican Party is a longstanding, robust, and diverse coalition. It will almost surely survive the chaos that the Trump nomination has revealed within its ranks.

We have gained an unusual window into chaotic and conflicting coalitions in the party, but the chaos doesn't mean the party is in peril. The chaos is just more apparent than it usually is in democracy. Democratic institutions often prevent us from seeing this chaos, but they don't prevent it from existing.

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