Broockman explains the problem as follows:

A voter’s ideal policy is significantly more extreme than the legislator’s on each of two policies. However, when mapping their views to one dimension it is the legislator who appears extreme. Why? When asked whether he would like to nudge the policy status quo in a conservative or liberal direction, this voter gives inconsistent answers, answering in a liberal manner on one question and a conservative manner on a different question. “On average,” then, this voter is in the ‘middle’ of the liberal-conservative continuum.”

One voter might support liberal policies calling for much higher taxes on the rich and also support a conservative stand in opposition to same-sex marriage. When the two responses are averaged, though, he or she would be defined as a moderate.

Meanwhile, let’s say that our hypothetical voter’s congressman supports relatively conservative policies in both cases and reliably casts relatively conservative votes. Because of the legislator’s ideological consistency, he or she is estimated to be " ‘extreme’ on the continuum,” as Broockman puts it. But who is actually the extremist?

Earlier this year, to further strengthen their case, Broockman and Ahler designed and conducted an innovative online survey of 1,240 respondents recruited by Survey Sampling International. The survey asked voters not only whether they supported the Democratic, centrist or Republican positions on a range of issues, but also offered respondents the option of taking more extreme positions – further to the left or right — than most Democratic and Republican members of Congress would be willing to support.

In the case of taxes, for example, the survey offered respondents seven choices, of which four were “extreme.”

The extreme choices on taxes on the left are: to establish a maximum annual income, with all income over $1,000,000 per year taxed at a rate of 100 percent, and to decrease federal taxes on the poor and provide more services beneﬁting the middle class and the poor; or to increase federal income taxes on those making more than $250,000 per year to pre-1990s levels (more than 5 percent above current rates). Use the savings to signiﬁcantly lower taxes and provide more services to those making less and to invest in infrastructure projects.