# Is Trump pulling the GOP right? A Median Voter Theorem discussion

Is Donald Trump’s presence in the GOP presidential race for 2016 pulling the GOP farther right?  In preparation for the first debate coming up on Thursday, August 6, I thought it would be fun to apply a little Median Voter Theorem (MVT) to the question.

As a quick overview, MVT says that under certain conditions, political candidates will adopt policies toward the middle of the political spectrum to capture the most number of votes.  Take a simple example: suppose three friends want to go to dinner, and their only concern is how far the restaurant is.  Friend A wants to have a quick drive, so prefers the closest restaurant.  Friend C wants to have a long drive to chat up old times, so prefers the farthest restaurant. Friend B wants to have a chat but not too long of a chat, so prefers a restaurant farther than A’s place but closer than B’s place.  MVT says that the friends will go to B’s restaurant, since it is the closest to their first choice preference.

Now, how to apply similar principles to the GOP debate? Five Thirty Eight has an article that includes some recent results from YouGov, who asked voters to quantify the degree of “conservativeness” of the candidates with the most liberal GOP candidate (George Pataki) rated as 50 and the most conservative candidate (Ted Cruz) scoring 72. (Note: Five Thirty Eight did their own measurement of conservativeness of the GOP candidates, but excluded Trump – more on that in a bit).  If all candidates were equally preferred on all counts except conservativeness, then the candidates would be best served by transitioning toward a degree of conservativeness around 61 – in the middle.  But we all know that some candidates are more popular than others.  As of the time of this writing, Fox News had announced the debate line up but not the actual poll numbers.  The New York Times released a prediction of who would be in the debate along with their actual poll numbers that ended up being 100% accurate, so I used the NYT numbers to weight the values of conservativeness.  Graphically it looks something like this:

As you can see, the NYT poll results are on the Y axis (values are percentages) and the voter assigned Conservativeness value is on the X axis.  The single peak at 63 is Donald Trump; the peak at 60 is Jeb Bush and the peak at 70 is Scott Walker.

Now, when applying the blunt tool that is MVT, one would assume that a GOP voter’s first preference would be the candidate closest to their own degree of conservativeness.  Their next preference would be the candidate second closest, then third closest, etc.  One would also assume that voters, wanting a winning candidate, would also factor into their choices a candidate’s popularity as measured by polls.  In other words, if a voter likes candidate A, but candidate A is unlikely to win, and candidate B is next closest in ideology but is also unlikely to win, then the voter would keep going down the list to a candidate that is closest to their conservativeness and likely to win.  Conversely, if you are a candidate, you will do your best to shift your ideology to be the best conservativeness match to the most voters, and therefore be the candidate most likely to win.  With this back and forth of shifting preferences by voters and shifting ideologies of candidates, an average conservativeness weighted by the candidate’s popularity can be used to approximate the optimal degree of conservativeness.  With this methodology, the new likely winning degree of conservativeness is not 61, but about 64.5 – 5.7% more conservative.

But is this due to Trump, or due to the GOP becoming more conservative?  MVT does not work as well in this case, since the data is not really single peaked around one candidate anymore (a key assumption for our basic MVT here) but double peaked around Jeb Bush and Scott Walker.  With those caveats aside, if you simply remove Trump and his supporters from the weighted averages, the new likely winning degree of conservativeness shifts right to about 65 – 6.6% more conservative than our original estimate of 61.  That would suggest that Trump is preventing the GOP from going even farther right, an interesting thought that deserves some additional thought.

The key point of contention here (besides any gripes political scientists might have about MVT’s accuracy) would be how one thinks Trump’s presence affects the GOP candidacy environment.  Ostensibly Trump is actually keeping the GOP from moving too far right because he is omnipresent, blunt, and grabs attention.  All media sources are discussing Trump all the time – he overshadows the other candidates, most of whom are categorized as more conservative than he is.  Without Trump, assuming his voters are not allocated elsewhere, the top three candidates become Jeb Bush, Scott Walker, and a tie between Mike Huckabee (71 conservativeness) and Ben Carson (65 conservativeness) with Ted Cruz, the most conservative, not far behind.  The political conversation and coverage could ostensibly be considerably more conservative.  On the other hand, because Trump is omnipresent, blunt, and grabs attention, perhaps this enables other candidates to become more radical and more shocking in an attempt to grab a piece of the small spotlight not already occupied by Trump.  This could in itself also make the candidates shift their ideology farther right.

So, to answer the initial question: according to the MVT, no, Trump is not pulling the GOP right.  How accurate is this portrayal? Only time will tell…maybe.