Disclaimer. Don't rely on these old notes in lieu of reading the literature, but they can jog your memory. As a grad student long ago, my peers and I collaborated to write and exchange summaries of political science research. I posted them to a wiki-style website. "Wikisum" is now dead but archived here. I cannot vouch for these notes' accuracy, nor can I even say who wrote them. If you have more recent summaries to add to this collection, send them my way I guess. Sorry for the ads; they cover the costs of keeping this online.
Krehbiel. 1998. Pivotal politics.
Krehbiel calls his model pivot politics theory because in collective choice settings where issues are well-defined and decision-makers' preferences are well-ordered, a specific decision-maker is shown analytically to be pivotal to the final policy choice. He argues that divided government does not explain why and when gridlock will occur (i.e. parties don't matter), but that his model of pivotal voters does, in addition to explaining why bills pass with greater than minimum-majority size. (This is more or less a quote from ch 1.)
Why does gridlock regularly occur in Washington? (Attempts to explain what he defines as two basic facts: (1) Gridlock usually occurs but not always; (2) Winning coalitions are almost always bipartisan and usually greater than minimum-majority sized.)
Gridlock occurs regularly because of moderate status quo policies, supermajority procedures, and heterogeneous preferences. Winning coalitions are usually greater than minimum-majority sized because of supermajority procedures.
The model assumes that all players can be arrayed along a unidimensional policy space. Parties are not a party of the model, and the status quo is assumed to be exognously given. Furthermore, the game is not repeated (formally).
Players: The most important "pivotal players" are the median member of Congress (not clear which house), the (Senate) filibuster pivot, the veto override pivot, and the president. Although there could be a veto override pivot and a filibuster pivot on either side of the median pivot, the only relevant players are the veto override pivot on the same ideological side as the president and the filibuster on the opposite side.
Sequence of play: Intuitively, it works something like this. The median pivot moves first, choosing either a new policy or the status quo. The filibuster pivot then decides whether to sustain or block a filibuster attempt. Next, the president decides whether to veto. If he signs the bill, the game ends; otherwise, the veto override pivot decides whether to override the veto. Gridlock can occur at any stage; the places where gridlock can be broken are (1) if the president signs the bill or (2) if the veto override chooses to override the veto.
Equilibria: The figure on pg 35 summarizes the general theory. Assuming the president is to the right of Congress, then you have preferences ordered as F - M - V - P. (Note that the veto override pivot and the president might be reversed; if so, substitute "P" for "V" in the discussion below.) As shown in figure 35:
Since the gridlock range includes all status quo points between F and V (or P), this implies that moderate policy proposals will tend to fall in the gridlock range. Thus, it isn't surprising that presidents often have a brief "honeymoon." Their election changes the alignment of preferences, so some policies that were inside the gridlock range (by the end of the previous president's term) might now be outside of this range, allowing the president and Congress to rapidly identify these policies and move them into the gridlock interval. But after this brief burst of activity, the president will find a decreasing number of policies that can actually be changed given the current alignment of preferences.
Moreover, those changes that are made will tend to be incremental. Unless the status quo is quite far from M, the result of policy change isn't likely to be M; it is more likely to be close to F or V (or P). Thus, despite initial excitement about a candidate's bold proposals, the realities of pivotal politics are likely to mean that actual policy changes will be incremental and passed by supermajorities.
In General, Krehbiel argues against party-centered theories (numbers 1-4 below), and also against other social choice theories (numbers 5-6):
Arguing on the same side as Mayhew (1991): the legislative outcomes of divided and unified government are about the same.
Research by the same authors
Research on similar subjects