New York, NY - Following the Illinois primary, I assume there will be renewed calls for either Rick Santorum or Newt Gingrich (and most likely the latter) to drop out of the race in order for conservative Republicans to increase their influence on the party's nomination process. The logic of the argument is very intuitive: as long as Santorum and Gingrich split the anti-Romney conservative vote, Romney can keep winning primaries with less than majority support.
Let me suggest a reason why it might be possible that the conventional wisdom is wrong, based on two simple assumptions:
Assumption #1: Neither Santorum nor Gingrich can get the required 1,144 delegates to win the nominating process and therefore their only hope of winning the nomination is to go to a brokered convention, where anything could conceivably happen.
Assumption #2: While, in any given state, Santorum (or Gingrich) is likely to get more of Gingrich's (or Santorum's) supporters should the other drop out, he wouldn't necessarily pick up all of his rival's supporters.
The first of these assumptions is now generally taken as a given, so should not be particularly controversial. The first half of the second point is potentially debatable - and might be more so in particular states - but, without it, the whole "the other guy should drop out" argument makes no sense either. So, in the interest of trying to debunk the "one of them should drop out" conventional wisdom, I'm just making this assumption explicit and noting that we need to believe it to be true for this debate to even matter at all.
To the extent we take the first assumption seriously, it is clear that the only viable strategy at this point for either Santorum or Gingrich is just to deny Romney delegates. At the end of the day, it really does not matter who gets those delegates between Santorum, Gingrich or even Paul: every delegate that Romney loses is a step closer to denying him the 1,144 delegates he needs to clinch the nomination. Therefore, it is a step closer to the only viable way for "anti-Romney" forces to get a nominee who is not Romney.
So now the question is simply reduced to the following: what is the best strategy for Santorum, Gingrich and anyone else who wants to keep Romney from being the nominee to reduce the number of delegates received by Romney? At this point, the actual rules used by states to award delegates become crucial.
For states that simply award delegates proportionally, Santorum and Gingrich need each other to stay in the race. This follows from the second part of my second assumption: as long as any Gingrich (or Santorum) voters would switch to Romney if Gingrich (or Santorum) drops out, then the "anti-Romney" forces are better off having both candidates still in the race, driving down the proportion of the votes won by Romney - and thus the number of delegates he can claim.
To illustrate this point, consider a simple example of a state we'll imaginatively name "Santokota". Imagine Santokota has 100 delegates to award and will go 50 per cent for Santorum, 30 per cent for Romney and 20 per cent for Gingrich. If the election is held without Gingrich dropping out, Santorum gets 50 delegates, Romney 30 and Gingrich 20.
Now imagine, just for the sake of the argument, that Gingrich voters would go 3:1 (and this is probably a good deal higher than it would actually be) for Santorum. Then a Santorum versus Romney contest (following a Gingrich withdrawal) would yield a stunning 65 per cent to 35 per cent win for Santorum, thus earning Santorum 65 delegates and Romney 35 delegates. This looks like a more convincing win for Santorum - and indeed wins him more delegates - but the goal here is not for Santorum to win delegates, it is to deny Romney delegates.
And in this respect the strategy has failed: with Gingrich in the race, Romney gets only 30 out of 100 delegates; with Gingrich out, Romney gets 35 delegates. Thus if Santorum's only shot at the nomination involves denying Romney 1,144 delegates, in a purely proportional contest, he is better off having Gingrich in than out.
However, not all states award their delegates proportionally. Some are instead "winner-take-all", where all of the delegates go to the candidate who wins the most votes in the primary. Here's (finally) where the Hungarians come in. Hungary uses an electoral system - which has been called the most complicated in the world - for its parliament that involves both proportional districts and single-member winner-take-all districts.
When I was observing Hungarian elections in the 1990s, it was not uncommon to see two parties that potentially planned to co-operate with each other (in this case, form a coalition government) competing with each other in the proportional districts but not competing with each other in the single-member districts. The way they would do this would be for the parties to strategically withdraw candidates in districts where they expected their allies to perform better than they would, with the assumption being that if their candidate could not win that particular seat, then perhaps their voters could help their allied party's candidate win the seat.
In this case, the two parties had a common goal: they wanted to assure that their two parties combined got a majority of the seats in the parliament, although of course, each party also wanted to maximise the number of seats they individually received.
There is an interesting parallel to the Republican nomination process here. If we assume that both Gingrich and Santorum share this common goal of denying Romney the 1,144 delegates, then it perhaps follows they should try the same strategy. As I just suggested previously, in proportional races they should both stay in the race. But in winner-take-all primaries, whomever is less popular (which would likely be Gingrich in most, but perhaps not all, cases) should drop out.
This would probably be radical in the US context - and I'm not even sure if it is technically possible, although I'm not sure why it couldn't be (after all, Santorum and Gingrich are both still "in" but neither ran in Virginia) - but it might just be the single best strategy for denying Romney the nomination before the convention.
It is, of course, worth noting that not all of the primaries are simply proportional or simply winner take all: in some states there are minimum votes needed to participate in the distribution of proportional seats, and in other states I believe there are thresholds above which a single candidate gets all of the votes.
Perhaps most interesting are the states where delegates are distributed not at the state level, but instead in sub-state level "districts" (often congressional districts). In these cases, Santorum and Gingrich might want to withdraw on a district-by-district basis, if that is somehow possible under current state law.
I will leave it to others who are better versed in the peculiarities of state's delegate rules to propose the appropriate strategies on a state-by-state basis. But I think the underlying point is worth considering: the best (and perhaps only) path to a non-Romney Republican nominee for president may lie in all of the remaining candidates staying in the race overall, but selectively withdrawing from particular contests, be it at the state or district level.
To put this another way, it may be time for Santorum, Gingrich and Paul to collaborate with one another in terms of how exactly to stay in the race, as opposed to calling for each other to leave it.
Joshua A. Tucker is a Professor of Politics at New York University, a National Security Fellow at the Truman National Security Project, and a co-author of the award winning politics and policy blog The Monkey Cage, where an earlier version of this article was posted.
Follow him on Twitter: @j_a_tucker
The views expressed in this article are the author's own and do not necessarily reflect Al Jazeera's editorial policy.