Recovered Space vs. Real Political Space
I am sick up and fed with reading papers in poli sci that confuse the recovered space of political action in legislatures with the actual space of political conflict in the society.
This problem has been analyzed in various ways, but two of the most orthodox are Hinich and Munger (1994, Michigan), Ideology and the Theory of Political Choice, and Poole and Rosenthal (1997, Oxford) Congress: A Political Economic History of Roll Call Voting.
Hinich and Munger argue that any empirically recovered space will have dimension one less than the number of effective parties, if those parties are coherent. That is, imagine a complex n-dimensional space of “real” preferences. Now, imagine two parties are points in this space. The line intersecting the two points (and that is what a recovered space is) will have dimension one, like any line.
Poole and Rosenthal back this up, and add quite a bit more useful information about changes over time. If a party is NOT coherent, or cohesive, there may be factions, and so more than one dimension, even in the recovered space.
(Now, let's be fair: the technique of Poole and Rosenthal is much older than the H&M contribution, and Keith rightly attributes the original idea of "what if there are just different spaces?" to Peter Ordeshook, in the 1960s. Here is a very cool, and intellectually honest, history of the idea)
Now, the underlying “true” space can be very complex indeed, and interest groups and outside forces constantly try to get past the filters imposed by agenda control of calendars and committees in the legislature.
If they do, or if the legislators’ own beliefs intrude, the recovered space may reflect these tensions.
The money point: I would expect scholars to recognzie the problem of using the recovered space (and NOMINATE is certainly one such) as a metric for understanding national politics. What it is, is a measure of the voting patterns of legislators on issues that are allowed to come to the floor for a roll call vote. The author will need to point out the shortcomings of recovered measures, and explain the mapping from real issues into NOMINATE space.
Then, it will be easier to discuss the difference (made much of here) between introduction of “new” dimensions as heresthetic manipulation or genuine cross-cutting cleavages. The gate-keeping roll of the majority party, legislative calendars, and the Rules Committee are key factors in keeping out the contagion of new issues just for heresthetic purposes. But it is much harder to isolate the chamber from the “real” pathogen of genuine cleavages within the party.
I do not mean to minimize the P&R contribution. To be fair, they make no claim to be measuring the OVERALL ideology of the society. And their technique is rightly accorded great respect as the primary measure of legislative voting patterns over time in the U.S.
But I wish that users of that measure would be as careful as its creators.