Ok explain this to me political scientists

The Median Voter Theorem is an explanation of how politicians choose to position themselves with respect the preferences of the public and how policy outcomes are then generated.  MVT assumes that voters are spaced along a continuous interval with respect to a specific policy.  So for example if you were to poll voters on what should be the maximum marginal tax rate there will be a distribution of voters from a 0% tax rate to a 100% tax rate.   Maybe the distribution looks like a bell curve, or maybe it has two humps, or maybe it looks like a chi square distribution.  In any case MVT then posits two politicians (or parties) who are each attempting to capture the votes of 50+% of the population or in this case 50+% of the area under the distribution.  Each politician chooses a policy value (for example a 20% marginal tax rate).  We assume that a voter will vote for the politician who positions his policy choice closest to the voters preference.  So if a politician A is at 20% and politician B is at 21% and the voter prefers 30% then that voter will vote for politician B.  The result of this is that the two politicians will push their policy choices toward the median voter (ie the voter who gives them 50+% of the distribution).  Hence policy outcomes end up reflecting the preferences of the median voter.

So how do we explain this?   The Republican strategy was not to only stop bills that are philosophically objectionable to the right but stop every bill possible.  That is what we have seen over the last few years as President Obama has repeatedly adopted Republican proposals only have the originator of the proposal oppose the policy once the President signals his approval of it.  There are many examples of this; Gov. Romney opposing Romneycare, Sen. McCain opposing cap and trade, a summary of some such proposals, this one, this one, this one, and this one is funny.

How does this behavior square with the median voter theory?   Party R initially chose a policy point on the distribution.  If party D moves towards R's policy point then party R moves back toward the right side of the distribution.  Under the basic MVT this movement by R would necessarily result in them getting a reduced share of the area under the distribution.

Perhaps an augmented version of the MVT would instead assume a two humped distribution and if a party chooses a policy too far from a voter then he loses that voter's votes even if his policy position is more favorable to the voter than is the policy position of the other party.  This could potentially mean that the two parties would not converge on the median voter.   Something like the drawing below.  Party R gets the red area and Party D gets the blue area.  In this case Party R moved too close to the center and hence lost the far right side of the distribution - even though those voters should prefer R to D.  Hence R's optimal strategy should be to move further right as they would gain more from the right hand side of the distribution than they would lose in the center.



However from the story that does not really appear to be the strategy consideration going on....  Whatever is the case this is certainly not vanilla MVT.