O’Brien, Leno and Letterman starring in the late night wars
January 29th, 2010While driving to and from Monroe, listening to National Public Radio about the Conan-Leno war, someone in an interview mentioned that Letterman may end up the loser if Conan moves to Fox to compete in a three-way war with Leno and Letterman straight up. Letterman may end up the real loser because while Letterman may beat Leno and Conan in head-to-head contests, he may get squeezed out, in a three-way fight. This is an application of Harold Hotelling’s median-voter work (‘Stability in Competition,’ Economic Journal, 1929).
Conan may be preferred to Letterman, who in turn is preferred to Leno by the young viewers of late night talk television. At the same time, we see Leno (J) preferred to Letterman (D), who in turn, is preferred to Conan (C) among older viewers. Instead of the left to right competition in the spatial competition among candidates, think of viewers, arrayed young to old, and viewers with four types of preference profiles: 1) C>D>J viewers; 2) D>C>J viewers; 3) D>J>C; 4) J>D>C, where “>” means “preferred to.” If there are more type 1s than 2+3s and more type 4s than 2 +3s but still more 1 + 2 +3s than 4s and more 2+3+4s than 1s, then Dave may dominate each in a head to head but be the loser in a 3 way race. This is straight from a Hotelling’s spatial competition (along a single dimension), though I do not think Hotelling did the 3 competitor case.
Here is a numerical example with made-up numbers.
Customer types
& market shares
1) C>D>J; 42% D v J D v C C v D v J
2) D>C>J; 10% 62% v 38% 58% v 42% 42% v 20% v 38%
3) D>J>C; 10%
4) J>D>C; 38%
With the distribution of customer types that we have in the example above, Dave Letterman dominates both Leno and O’Brien in head-to-head matchups, with 62-32% with Leno and 58-42%. However, in a three-way battle for late night talk show viewers, it would be quite possible for Dave to go from first to last if Conan on Fox and Leno on NBC compete in the exact same time slot as Dave.
If these were candidates, then things become very unstable, as the left- and right- wing candidates maneuver toward the middle, making the moderate candidate’s position unsustainable, and she gets driven from the campaign. Late night comics, though, have a more difficult time shifting positions, changing their appeal to different audiences.
I should mention that it would also be possible for Letterman to continue to dominate the other two, if there were more of the middle two types than the two extremes.
-MC
