To measure that, they conducted a survey in which they asked respondents' opinions on victims and on offenders, assessing their support for each framework. They also inquired about their political opinion (on a conservative to liberal scale).
To measure gut reactions, rather than calm reasoning, they asked respondents these questions under cognitive load (made them memorize an 8-digit number while they responded). They found that the satisfaction with restoration, whether on its own or as added to satisfaction with retributivism, goes up for liberals and down for conservatives with cognitive load.
Their conclusion was, therefore, that liberals and conservatives have different intuitive reactions to serious crime: Liberals endorse restoration while conservatives favor retribution.