The median voter theorem is just a mathematical conclusion from a set of simple assumptions, it can’t be watered up or down. If some set of voters rank proposals on a single axis with single-peaked preferences then the only Condorcet winner will be the median voters ideal point. The key here is that the voters choose the axis on which to rank the proposals. The voters can rank the candidates on any axis, taxes or policies or height. Usually smarter actors rank proposals and candidates on an ideology axis by collapsing issues onto one axis, as a mental heuristic. But if they interpret the axis as “does he run ads where he shoots guns” instead of “does he vote for my tax rate”, the gun ads determine the axis not the tax rate. In this case the assumption is that Republican primary voters care a lot about the Trump-support axis.
The two level game papers are cool, but not relevant here.
The MVT is important here because Trumps influence over represenatives is non-linear with his vote share. If Trump loses 20% of his primary influence and loses the median primary voter, he does not lose 20% of his influence, he loses most of his influence.
1, The “watering down” comment was really referring to the idea of expanding the “preference axis” assumption to include more than just policy, to the extent that MVT changes from “Politicians moderate their policies towards the center of policy axes” (which would be a perhaps unintuitive claim that doesn’t need explicit reference to “MVT”) to “Politicians appeal to the majority of the voting public” (which is almost “no-duh” except that it irons over potential wrinkles, like “someone who is very far right/left won’t even bother voting unless one of the candidates moves far enough towards them, rather than spending their time to go out and vote for the ‘less bad candidate’ in an election which they might deep down recognize they won’t actually have any impact on...”).
Ultimately, I think the question of whether Berkowitz should have discussed MVT by name is less important that the question of MVT’s validity, but I’m not in an epistemic position to get deeper into the weeds on that. 😶
2. I still don’t see that as a true “silver bullet”; I imagine Berkowitz might consider it one of the potential positive reforms, though.
Original median voter theorem paper, Duncan Black in 1948
Let us suppose that a decision is to be determined by vote of a committee. The
members of the committee may meet in a single room, or they may be scattered
over an area of the country as are the electors in a parliamentary constituency.
Proposals are advanced, we assume, in the form of motions on a particular topic
or in favor of one of a number of candidates. We do not inquire into the genesis
of the motions but simply assume that given motions have been put forward.
In the case of the selection of candidates, we assume that determinate candidates
have offered themselves for election and that one is to be chosen by means of
voting. For convenience we shall speak as if one of a number of alternative mo-
tions, and not candidates, was being selected.
Let there be n members in the committee, where n is odd. We suppose that
an ordering of the points on the horizontal axis representing motions exists,
rendering the preference curves of all members single-peaked. The points on
the horizontal axis corresponding to the members’ optimums are named O, 02,
03, . . . , in the order of their occurrence. The middle or median optimum
will be the (n + I)/2th, and, in Figure 3, only this median optimum, the one im-
mediately above it and the one immediately below it are shown
Anyway, this is really a pedagogic question. How best should we teach politics? Some people advocate that we should disregard the MVT because it is both “obvious” and “false”. Setting that contradiction aside, I think the underlying assumption that only theories with perfect data fit should be taught is wrong. By the same logic, physics should not teach Newtownian mechanics because it is wrong relative to quantum mechanics. You can’t just give the reader quantum mechanics, you need to start with a theory they can understand then update it.
The median voter theorem is just a mathematical conclusion from a set of simple assumptions, it can’t be watered up or down. If some set of voters rank proposals on a single axis with single-peaked preferences then the only Condorcet winner will be the median voters ideal point. The key here is that the voters choose the axis on which to rank the proposals. The voters can rank the candidates on any axis, taxes or policies or height. Usually smarter actors rank proposals and candidates on an ideology axis by collapsing issues onto one axis, as a mental heuristic. But if they interpret the axis as “does he run ads where he shoots guns” instead of “does he vote for my tax rate”, the gun ads determine the axis not the tax rate. In this case the assumption is that Republican primary voters care a lot about the Trump-support axis.
The two level game papers are cool, but not relevant here.
The MVT is important here because Trumps influence over represenatives is non-linear with his vote share. If Trump loses 20% of his primary influence and loses the median primary voter, he does not lose 20% of his influence, he loses most of his influence.
There are better ways to select leaders, but our current leaders choose not to influence them. Our current leaders like the current leader-selection system because they win at it. (See paper)[https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1467-9248.2005.00514.x?casa_token=R0YSBl-4UKQAAAAA:pwa_9ENFHN8VU9PT50ymM6R1fy57NtdDSW1R7K5aeT8tGXMRvLzwHzkAoFh7di80Lp4mv8b4e8ZnFWg]
1, The “watering down” comment was really referring to the idea of expanding the “preference axis” assumption to include more than just policy, to the extent that MVT changes from “Politicians moderate their policies towards the center of policy axes” (which would be a perhaps unintuitive claim that doesn’t need explicit reference to “MVT”) to “Politicians appeal to the majority of the voting public” (which is almost “no-duh” except that it irons over potential wrinkles, like “someone who is very far right/left won’t even bother voting unless one of the candidates moves far enough towards them, rather than spending their time to go out and vote for the ‘less bad candidate’ in an election which they might deep down recognize they won’t actually have any impact on...”). Ultimately, I think the question of whether Berkowitz should have discussed MVT by name is less important that the question of MVT’s validity, but I’m not in an epistemic position to get deeper into the weeds on that. 😶 2. I still don’t see that as a true “silver bullet”; I imagine Berkowitz might consider it one of the potential positive reforms, though.
Original median voter theorem paper, Duncan Black in 1948
Anyway, this is really a pedagogic question. How best should we teach politics? Some people advocate that we should disregard the MVT because it is both “obvious” and “false”. Setting that contradiction aside, I think the underlying assumption that only theories with perfect data fit should be taught is wrong. By the same logic, physics should not teach Newtownian mechanics because it is wrong relative to quantum mechanics. You can’t just give the reader quantum mechanics, you need to start with a theory they can understand then update it.