The Topology of US Elections: why politicians must lie, er, flip-flop to be elected

Mike Smitka, Economics, Washington & Lee Univ

Under the US primary system for Congress and the White House, politicians must flip-flop in order to be elected. Now candidates may be dishonest in the normal sense of the word. But if a candidate truly wishes to be elected – surely most do! – then they must change their positions during the course of a campaign. That's not healthy for our political system.

Economics helps explain why.

Put every voter on a line from right to left – a typical assumption by those watching campaigns. Theory (and longstanding observation) suggests candidates gravitate towards the center. With a bit of added detail, this model, due to Hotelling, helps clarify the strategic nature of our electoral game. (Harold Hotelling's simple model of product differentiation dates to 1929. In political science it's know as the median voter theory.)

... our political system FORCES candidates to flip-flop to be elected ...

Let me introduce the "classic" version: where on a small beach would two pushcart vendors locate? Assume they start on the ends of the beach, one on each side. They then split the business – everyone goes to the nearest vendor, with the person in the very middle indifferent which he chooses. But let one vendor push his cart partway towards the center, and that cart then splits the business that lies between, plus everything towards their end, and so gets more than half the business. The response is obvious: the other cart moves towards the center as well. Repeat, and eventually they're next to each other, at the center of the beach.

The political analog is obvious. Entering a general election, candidates initially start with positions that appeal to their party's base. That reflects the need both to raise funds and to mobilize volunteers. However, to win a general election they need to appeal to a broad array of potential voters, while keeping their base energized. That produces a lot of tension.(Duverger's Law states that you find only two political parties in an electoral system of single member districts, such as in the US. In contrast when Japan had many 5-member districts, a candidate needed only 1/6 of the vote to be elected, and general elections saw both many more than 5 candidates and an array of small parties. Subsequent electoral reform eliminated those, and most of the small parties vanished.)

In the US, however, we are (to my knowledge) unusual in having a two-stage electoral process for Congressional seats and the President. So let's look at an election to Congress. That process starts with primaries; there's lots of local variation, but for simplicity assume they're limited to party members. Now voting is inconvenient, and primaries don't always get much publicity. Only those who really care vote. Candidates align themselves at the center of their party, and so we get one candidate at the 1/4 mark, another at the 3/4 mark. He/she who can move most successfully to the center wins the popular vote. If one candidate missteps and does not quite move to the center, the other candidate can take advantage of that. Of course random factors matter – an untimely scandal, spending money unwisely, misjudging which states are on the edge and so not allocating enough time, or even personality. Then there's gerrymandering. The model doesn't capture everything.

This simple model does highlight the dilemma Republicans face. The primary system pulls them to the right, where the issue of race (plus, less centrally, social nostrums and issues of the moment) incites anger, attendance at political rallies, we all know what is happening. With multiple candidates, the challenge is to mobilize a large enough block of activists to turn out to vote, while appealing to various specialist interests (the gun lobby, the anti-abortion lobby, the wealthy seeking yet more tax breaks). Multiple candidates guarantee that no one can so much as nod at the center, at least in the heat of the early primaries. This time around, there is only one viable Democratic candidate, who can safely ignore the far left and stake out a position close to the center. Even a weak candidate can win. Put in a strong candidate, a good campaigner such as a Bill Clinton or a Barack Obama, and you have a landslide. (Strong candidates and strong presidents aren't the same thing – we elect people because they're good at campaigning, and they may be lost on policy, bad at day-to-day administration and inept at negotiating with Congress.) Candidates can't do away with party activists, at least when the primary campaign is contentious. However, the party faithful will then be unhappy with their final candidate, because the median activist isn't a centrist.

Now lots of assumptions are hidden in this model. However, we don't need a perfectly uniform distribution (you stretch out the line to pull down any humps). Going beyond one dimension is possible, but with more caveats. We can make other modifications, by for example allowing candidates to "buy" votes. Of course two can play that game, and this collapses to our base Hotelling / median voter model if it's harder to buy votes the further you are from a potential voter's position, which I judge to have been the case in the 19th century.

However, the model does require flexibility; voters opt for whomever is closest to them, even if they're at one end of the spectrum and the candidate is all the way in the center. In other words, no one running for office gets locked into their initial positions. (In industrial organization, the Stackelberg model, a standard of textbooks, assumes that's not the case.) A second crucial assumption is that there are only two players; three's a crowd, and there's no equilibrium strategy. Third, if the market is a circle rather than a line, then two players move as far apart as they can, the opposite result – but in my judgment that's not how politics works, even if the extreme right and the extreme left may be hard to distinguish – think Weimar Germany, where both the right and the left were nascent dictators and central planners, or in the US the political activist Lyndon Larouche, who seemed to move from far left to far right without blinking.

So why are our politics right of center rather than centrist? (To those outside the US, Obama looks like a standard, big-party conservative rather than a member of the party on the left.) First, there seems to be a limit on how quickly (that is, how far) a candidate can re-center after the primary. In terms of the Hotelling model, if voters are limited in how far they will travel – they won't vote for someone who "betrays" them – then candidates will be limited in how far they can reposition themselves after the primary election. (In the Hotelling model, this comes for example from using the square of the distance a voter must travel.) The harder it is for a Republican to shift away from positions needed to win a primary, the easier it is for the Democrats. But potentially the Democrats enter the race with similarly untenable positions. In fact, that seems not to be the case: casual empiricism suggests that while there is a distinct "Right" in American politics, there is no Left. Unlike Europe or Japan, the US has never had a strong Socialist Party, or even a Labor Party. (What "liberal" means is unclear, at least to me, except for its use as a pejorative by Republicans.) And that's an important point. Due to their diffuse positions those with some sort of "liberal" inclination have only a weak pull on a candidate, and a good grassroots campaign can turn out their vote.

But we do have splinter parties on the Left, with small Communist, Socialist and Green parties. That's good news for the Democrats, most of the time, because that means that there's not much Left left within the party (however strident claims to the contrary of the Right might be). In contrast, in the US there is no far right party (despite the "Tea Party" label, such individuals reside in the Republican Party). So Republican candidates have to worry about the rightmost extreme of the political spectrum, which Democrats have no Left left within their party with whom they have to contend. That makes the Democrats more centrist even in their primary elections. So if we incorporate that in the model, the Democratic Party primary victor will be more centrist, whereas the "Tea Caucus" activism results in a primary victor to the right of center even within the Republican Party. The result is that the entire electable political spectrum is pulled to the right of center.

In the last election, Republican candidates proved inept at flip-flopping, that is, did a poor job of moving to the center. Perhaps this was a defect in the candidates themselves, or in their use of the same political advisors they employed in the primary, who were unable to distance themselves from their "natural" constituency. However, it's not just been this one election. Rhetoric aside, in their votes in Congress and their policies as President, the Democrats seem to be center or center-right. The odd election when a third-party candidate has traction helps bolster this argument, as they then pull a block of voters who might otherwise be convinced to hold their nose and vote for a candidate too centrist for their tastes. The result is electoral disaster for one or the other party, as happened to the Democrats when Ralph Nader nibbled away at the more liberal part of their base.

Of course if being an incumbent get's you close to half the vote, then strategy doesn't much matter – an incumbent has to try hard to lose. Redistricting sometimes throws open the process. At least on the margins scandals can matter. In addition, for the House (but not the Senate) local issues have salience. In practice, though, that seems to mean that rural candidates are always pro-farmer, whatever their party label. In other words, on local issues competent candidates of all stripes move to the center and prove indistinguishable. In any case, to the extent that incumbency dominates other factors, the only elections where this Hotelling model matters are ones for open seats – whether one views Romney's candidacy as amusing or as sad, if incumbency really matters, it was doomed all along to irrelevance. This time around there is of course no incumbent in the presidential race.

To sum up, the Hotelling model suggests that a large swath of voters will always be unhappy with presidential candidates, come the general election. Our politicians are "slick" and "untrustworthy," flip-flopping, betraying those who worked for them in the primaries. Thanks to smaller electoral districts and hence a less diverse electorate – gerrymandering accentuates that – members of the House will also be more polar than the electorate as a whole. Granted, you always want to bargain down to the wire. But if the center dominates, then you do end up with a deal. That hasn't always happened in the past couple Congresses. This simple economic model suggests that all that is required to generate that result is the rise of a modest-sized "sticky" right. We won't know until the new Congress whether having Paul Ryan, one of their own, as Speaker of the House makes any difference. The political pundits I occasionally read opine not. That's what my model also suggests.

Addendum: Economics insists that models aren't sensible if they don't lead to equilibrium behavior. A "sticky" right opens room on the left for a third-party candidate, because it leads Democrats to move to the right of center. If political entrepreneurs succeed in finding issues that will unify those to the left, then the center can lose all salience. Now the right end of the US spectrum seems to have defined itself around racial and class lines, white and old and prosperous, together with a partially overlapping group of social conservatives. That's a shrinking base, but the Hotelling model suggests that as long as we maintain a system of party-oriented primaries, that base won't become irrelevant, at least for the House of Representatives.

One other implication is that in districts with strong incumbents, it's hard to motivate the average person who might vote for an opposition candidate. Only strongly driven voters participate – in other words, you get kooky candidates, who take positions incompatible with any sort of move to the center. That reinforces the strength of the incumbent...

Finally, as an economist let me propose a testable hypothesis: that in contested elections, we will frequently see a change of advisors between the primary and the general election for candidates who prove successful. In contrast, candidates who are unsuccessful will frequently have the same advisors throughout. This may be hard to test. House races are too small to have much staff, Senate campaigns may be little different (and with 6-year terms there are fewer). Presidential campaigns are but once every 4 years. So there aren't many data points.

An early version of this was posted to my Autos and Economics blog in August 2013 and then revised for my Economics of Strategy class in Fall 2013. For obvious reasons, I'm using this example for Winter 2016!