When Politicians Confuse Mean for Median

There's a sixty-year-old theorem called "The Median Voter Theorem." Russel Crowe had a part in inspiring it. The basic idea of the Median Voter Theorem is that, in a head-to-head election, a politician will maximize her votes on election day by adhering to the position of the ideologically median voter in the electorate. Each voter votes for the politician whose ideological position is closest to the individual voter's own position, so finding the median voter is the way to go. You get more votes by "moving to the center."

It's the type of political science theorem that annoys me (for one, it makes for a boring campaign season), but I grudgingly accept it as a winning electoral strategy. I bet that most American politicians of the two major parties pursue this strategy, and that most pursue it quite consciously. It works, but only if it's executed correctly. I think that a lot of politicians fail at the median voter strategy by confusing the mean for the median.

A lot of politicians make the mistake of thinking that they're running for office to represent the state of Platonia. It's kind of a comforting place, this state of Platonia. It's simple, too. With only 11 registered voters. There's a round and even ideological spectrum to it. You can even express each voter's ideological position with a number. 0 = most liberal person ever, while 10 = most conservative person ever.

Platonia Registered Voters and Corresponding Ideological Score (ID)

Voter	1	2	3	4	5	6	7	8	9	10	11
ID	0	1	2	3	4	5	6	7	8	9	10

Median Voter (#6) ID = 5
Mean Voter ID (55/11) = 5

Voter #1 and Voter #11 are incredibly ideological. They're not much for 5 IDs, or even 2 or 8 IDs respectively. They don't vote much, and when they do vote, it's for Lyndon Larouche or somebody like that. Voter #2 and Voter #10 have 1 and 9 IDs, respectively. They like guys like Ralph Nader and Ron Paul, but sometimes they'll vote for the major party candidate if that candidate makes a good case to them, or they perceive that their vote is too important this time around to "throw away." Voter #3 and Voter #9 have IDs of 2 and 8, respectively. Here is the beginning of each major party's base. Still, a certain level of ideological "purity" is required from the candidates to get their vote. Voter #3 cannot stand politicians who behave like they have a 6 ID, and Voter #9 cannot stand politicians who behave like they have a 4 ID. Voter #4 and Voter #8 have IDs of 3 and 7, respectively. Each considers herself a "Democrat" or "Republican" when asked her party affiliation. Each also doesn't perceive the other party's policies as good for her. Voter #5 and Voter #7 each say the he's "independent," but really each almost invariably votes for the same major party over and over again (Democratic and Republican, respectively).

Finally, there is Voter #6. Voter #6 is the median voter. This is the voter up for grabs and the voter that each major party candidate needs to capture in order to win. The closer Voter #6 perceives you to be, the more you maximize your chances at winning.

It's not that difficult to win an election in Platonia. You just need to do and say things that signal to Voter #6 that you have a 5 ID. If you're a Democrat, then you also signal and behave every once in a while in ways that show you have a 2, 3 or 4 ID. But don't act like you have a 6 or 7 ID too much. That will anger your base. You may capture that median voter still, but your base won't vote. It's not hard in Platonia, however. You can act like a 5 and win. And it's easier to act confidently as a 5 because 5 is the mean ideological score of Platonia. The political "climate" is perceived as a 5. The same holds true for a Republican candidate, but in reverse.

The campaigns are boring in the State of Platonia, but professional and effective.

But what about a less ideologically symmetrical state? Let's call this state ... oh, let's say the state of Kansaras. Kansaras, coincidentally, has only 11 registered voters.

Kansaras Registered Voters and Corresponding Ideological Score (ID)

Voter	1	2	3	4	5	6	7	8	9	10	11
ID	1	2	3	3	4	5	7	8	8	9	10

Median Voter (#6) ID = 5
Mean Voter ID (60/11) = 5.45

Compared to Platonia, Kansaras skews toward the conservative side. The mean Voter ID is 5.45 rather than 5. The median voter has a 5 ID, just like the median voter in Platonia.

So, let's say that a politician gets elected to the US Senate to represent Kansaras. He's a Democrat. His name is ... oh ... let's say Lance Blincoln. Senator Blincoln reads the political climate - the mean - correctly as a 5.45 ID. Senator Blincoln decides that by the time he is up for reelection, he should signal to the electorate by word and deed that he himself mostly is 5.45. This way, he will capture the middle.

Senator Blincoln figures that the best and easiest way to signal a 5.45 ID is to take ideological positions that, when averaged out, will put him near 5.45. Senator Blincoln says and does some things that a 3 or 4 would do, but also some things that a 6 or 7 and sometimes even an 8 would say or do. But when you tally-up all of Senator Blincoln's words and acts and divide, it all works out to an ID of 5.45. "Perfect!" thinks Senator Blincoln. "I am on my way to reelection."

But Senator Blincoln is not on his way to reelection. All of those 6 ID and 7 ID positions he's taken have angered the 2 ID and 3 ID voters. It does not matter to them that Senator Blincoln's positions average out to a 5.45 ID. Those 6 and 7 positions are just too much to bear, even if Blincoln has a fair amount of 2ID and 3ID positions to temper them.

Now, let's say that it's primary election time in Kansaras. Let's say that Senator Blincoln gets a primary challenge from another state-wide elected Democratic Lieutenant Governor by the name of ... Jill Walter. Interestingly enough, Jill Walter's ideological ID is the same as Senator Blincoln's: roughly 5.45. The difference is that Lt. Governor Walter's ID was arrived at by taking very few 6 ID positions, and totally avoiding any 7 positions. Most of Lt. Governor Walter's positions are in the high-4 and low-5 range. Lt. Governor Walter knows that the median voter is a 5ID voter, but also that she can't take too many 6 or 7 positions to anger the 2ID and 3ID voters if she wants their support. So, Lt. Governor Walter stays near-exclusively in the range of 4.0 to 5.9. This keeps her close to that median voter without turning-off the 2 and 3 ID voters.

Senator Blincoln can't believe it when he finds that his primary race against Lt. Governor Walter is turning out to be a nail-biter. "What about all of those 3 and 4 ID positions I took?" thinks Senator Blincoln with some consternation. "Have the Democratic voters forgotten? I'm the kind of 'moderate' Democrat that wins general elections in this state. My ID is 5.45: right in the middle. Sheesh!"

Even more perplexing to Senator Blincoln are head-to-head general election polls which show Lt. Governor Walter having a better chance against the likely Republican candidate than Senator Blincoln. "What's the deal? I'm just as much in the middle as Lt. Governor Walter!"

The deal is that Senator Blincoln confused the mean for the median, and confused the Platonia electorate for the Kansaras electorate. The electorate in Kansaras may skew more conservative (or liberal, in the case of Chassamusetts) than Platonia, but it doesn't necessarily follow that the median voter is more conservative (or liberal, in the case of Chassamusetts).

In Platonia, you can hop around more with your ideological positions, and still capture the median voter. If you take some 6 or 7 positions every once in a while, it's less likely to hurt your election or re-election chances. You might lose a 2 or 3 voter here and there, but the other candidate often will do the same on the other side. When the mean and median are the same, you have more lee-way.

But when the mean and median are different, you can't stray too far from either. In fact, the more you stay within the zone between the mean and median, the better. You're going to have to take a fair amount of 3 and 4 positions to keep those voters on your side, but you can't afford to take 6 or 7 positions to "average out" your mean. The 2 and 3 ID voters will decide not to vote for you. Your general election numbers will suffer. You won't win the election, even if your average position turns out to be right in the middle.

Senator Blincoln isn't the only person to make this mistake of confusing the electorate for Platonia's electorate, or confusing the mean for the median. "Conventional Wisdom" pundits make this mistake all the time as well. A politician can't just average-out a bunch of positions and call herself a "moderate," even if it averages out that way. Too many 3s or 7s will turn off the voters you need to win. The pundits may cheer your "principles" or your "maverickiness," but the voters you actually need to win will abandon you, or at least not be very excited about you.

John McCain (who averages-out quite conservative) found this out in 2008, when his high-profile 3ID and 4ID positions came to haunt him. He had to go out and find a solid 9 running-mate just to create some enthusiasm. Arkansas Senator Blanche Lincoln of Arkansas found this out just this Spring. Despite Senator Lincoln's positions "averaging out" quite near the mean and median, many of the regular Democratic voters she depends on for the general election got behind a different candidate in the Democratic primary. The candidate, Bill Halter, is roughly as "moderate" as her. But Halter rarely spoke or acted like a 6, and never like a 7. Halter came extremely close to defeating Lincoln. It took the great example of "5-ness," former President and Arkansan Bill Clinton, to rescue Lincoln by assuring the Democratic electorate of Arkansas that Lincoln was ideologically near them.

Still, Lincoln is likely to lose in the general election this November. It seems that too many regular Democratic voters, those 2s and 3s, will stay home due to Lincoln's 6 and 7 positions.

Whatever one thinks of the Median Voter Theorum as a strategy, it has to be executed moderately for it to work. Averaging out disparate positions to the middle will make you a loser on election night. Pundits may like you, but not voters.