Santorum hurt by Republican Delegate Selection Systems

The US presidential nomination and election system is profoundly undemocratic. The primary problem is money aka corporate power or capitalism.

The primary/caucus process varies greatly by state and the differences are HUGE. Delegates can be directly chosen by the primary, or there can be a process which requires a county convention followed by a state convention. Delegates can be bound (required to vote for a candidate) or completely unbound.

The Democratic nomination process is more democratic than the Republican one as it makes greater use of proportional voting.

The Republican system often uses winner take all at both the level of the Congressional District. This is undemocratic in of itself. However, what I'm interested in pointing out is a quirk in the system. Namely Santorum is winning more states that use a more proportional voting system, while Romney (and Gingrich) are winning states that use less proportional voting systems. This quirk is costing Santorum delegates.

For delegates, I'm using the CNN Delegate Estimates (VA Example). There are some large differences in delegate estimates for several states.

This chart shows the relationship between the % of votes that a candidate receives and the % of delegates that they get. Now while this is clearly NOT a linear relationship (as you gain more delegates when your vote increases from 40% to 50% than when it increases from 90% to 100%) this still shows that Santorum is getting less delegates than Romney for the same number of votes.

For instance, at 30% support Santorum will get around 30% of the delegates, but if Romney has 30% support he gets an average of approximately 38% of the delegates. So Romney is getting 27% more delegates per vote.

Gingrich is doing well in terms of delegates per votes, notably because he won landslides (in terms of delegates) in Georgia and South Carolina.

This chart shows the relationship between the candidate's lead and the percent of delegates that they get. If the candidate came in first place, then we calculate their lead by comparing them to the second place candidate. If the candidate is not in first, then they get a negative value that is the difference between their vote and that of the first place candidate.

I've approximated the relationship using a linear fit (which again isn't the most likely fit, but is the easiest to do).

This shows that with an equal lead, Romney gets more delegates than either Santorum or Gingrich. If Romney was tied first (eg had a 0% vote lead), Santorum would need to have an approximately 12% lead to get the same percent of delegates.

Disclaimers
I'm not saying the system is biased against Santorum. I'm saying he is unlucky (like the Conservative party in the UK which in past elections received far fewer seats than Labour for the same national vote share).

I use a linear fit which isn't the best method. I suspect the linear fit (for my first chart) has a negative bias for candidates who typically get low vote shares. So this might make Santorum's delegate per votes lower than it should be. I'd like to see analysis done using another form of analysis.

Testing the Negative Bias

I removed the cases where Romney had a high vote percent, and some of them where Santorum did poorly to compare how many delegates per vote they would be getting if they were getting roughly equal vote shares.

I removed NH, FL, NV, AZ, ID, MA, VA and WY. In the remaining states, Santorum got a total of 426.5% and Romney got 437.8% - a lot closer than full result (where Romney gets a total of 867.9% and Santorum 545.2%).

This, admittedly arbitrary test, shows a similar result as my original test. Romney gets more delegates than Santorum. However, this pro-Romney bias is less pronounced. For instance, if Santorum is at 30% vote he gets about 32% of the delgates, and Romney at 30% gets about 36%. This 4% gap is HALF of what the first model showed.

Ohio and Virginia
Part of Santorum's problem is that he didn't field a full set of delegates in Ohio. He didn't run in Virginia which actually helps him in this model (as getting 0% delegates for 0% vote is better than the model predicts). Though in real life, not running in Virginia caused Santorum to lose delegates and under-perform his potential.

Small National Poll Lead for Romney
Romney currently has a 32.5% to 28.1% lead over Santorum in the national poll. I think Santorum isn't doing as well in actual contests because he lacks money, organization (due to his late ascendancy to a second place candidate), and because Romney is hitting him hard in states one at a time. So typically Santorum has a big lead in a state (like Ohio) and then, after Romney outspends and out-organizes him, he loses it.