According to the Median Voter Theorem, a successful candidate is likely to reflect the typical (or middle) voter in any distribution of voters. Explain why and how primaries might lead to candidates who appear extreme to the median voter.
If the median voter theorem is correct, the only way that primaries can elect a candidate who is too extreme for the median voter is if there is a different set of voters in the primary than in the general election. In other words, the candidate is not too extreme for the median primary voter but is too extreme for the median voter in the general election.
The median voter theorem holds that the winning candidate is the one who best appeals to the median voter. Therefore, if the theory is correct, the winning candidate cannot appear extreme to the median voter in a given election. However, if there are different electorates in two elections, the candidate who wins the first election may seem extreme to the median voter in the second election.
This fits with what we know about elections in the United States. In general, primary elections attract smaller electorates that are more extreme in their views. Only the most interested voters tend to vote in primaries and the most interested voters tend to be more extreme in their views than voters who are mildly interested in politics.
This means that an extreme candidate could appeal to the median primary voter and then look extreme to the median voter in the general election. This is a perennial dilemma for candidates. They must figure out how to appeal to primary electorates without taking positions that make them unacceptable to the general election voters.