Sen. Ted Cruz (R-Tex.) marks the start of his presidential campaign by giving the convocation address at Liberty University in Lynchburg, Va., on Monday. (Jay Paul/Bloomberg News)

On Monday, Sen. Ted Cruz (R-Tex.) became the first major contender to announce his candidacy for the 2016 Republican presidential nomination. Dan Balz has written that Cruz’s candidacy “tests the limits of conservatism,” and based on his congressional roll call voting record, Cruz is the fourth-most-conservative member of the Senate. But how does his ideological position compare to those of Republican primary voters, especially in early states such as Iowa and New Hampshire? Very favorably, as we will see.

We use data from the 2014 Cooperative Congressional Election Study (CCES). The 2014 CCES asked respondents to place themselves and several political figures, including Cruz and former Florida governor Jeb Bush, on a seven-point ideological scale ranging from “very liberal” to “very conservative.”

Historically, a major problem with using this type of perceptual data has been that different people interpret the points on the scale to mean different things. For instance, a Democratic respondent might view the tea party as “extremely conservative”, while a Republican respondent might view the group as only “somewhat conservative.” When respondents distort the ideological scale, their self-placements are not directly comparable.

We address this potential problem using a method known as Aldrich-McKelvey scaling that corrects for such distortions and places voters and candidates on the same ideological scale. We use the resulting ideological scores below to make direct comparisons between Cruz and Republican voters in the early primary states.

Below is a graph of the ideological scores of self-identified Republicans in the early caucus and primary states of Iowa, New Hampshire, South Carolina and Florida using box-and-whisker plots. In a box-and-whisker plot, the range between the 25th and 75th percentile values is shown using a box, while the median value is shown using a dot inside the box. That is, 50 percent of Republican voters in each of these states have ideological scores within the corresponding box. The 5th and 95th percentile values are marked with the vertical dotted lines extending from the box.

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We use the solid vertical lines to mark the ideological scores of Bush (light red) and Cruz (dark red). Immediately clear is that Cruz is quite ideologically in-line with Republican voters in these four states. In fact, his estimated ideological score is to the left of (i.e., more liberal than) the median Republican in Iowa, South Carolina and Florida.

Instead, Bush is the candidate who appears to be the most ideologically out of step with Republican primary electorates in these four states. His score places him to the left of at least 70 percent of Republican voters in every state.

Of course, these results hardly mean that Cruz is better positioned than Bush or other candidates to win the Republican presidential nomination. For one, support from party insiders matter a great deal in the primary process. In addition, Cruz is not as widely known as other candidates in the field, and a long campaign season may serve to push perceptions of him further to the right. Finally, primary voters account for electability in addition to ideological distance in their voting decisions.

These results do indicate, however, that Cruz is quite ideologically compatible with Republican voters in key early states.

Robert Lupton is a political scientist at Michigan State University. Christopher Hare is a doctoral candidate in political science at the University of Georgia.

Note: The 2014 Cooperative Congressional Election Study was conducted by the survey firm YouGov in two waves last year — in October and November.  The sampling frame was American adults, and the sample size was 56,200.  Respondents were interviewed online. Further information about the YouGov sampling methodology is here and here.