Quotes are from Strom unless otherwise noted.

Chapter 1:

Goal: develop a theory to explain why, given a set of procedural rules and a set of individual preferences of each legislator, a legislature comes to the conclusions that it does.

We assume that actors (legislators) are rational and preferences are fixed.

We assume that, from any individual's point of view, each outcome has a utility (that is, any two outcomes are comparable in the individual preference relation, and the individual preference relation is transitive).

A 2D graphical representation of unidimensional preferences is to have the horizontal axis be various outcomes and the vertical axis be utility. For each individual, draw a line to represent their preferences.

Theorem (Black 1958): If the outcomes can be ordered so that the preferences of each participant, when drawn on this graph, are each single-peaked, then if you find the median peak (median along the horizontal axis), the corresponding outcome is the Condorcet winner.

In general it is possible for there to be no Condorcet winner, that is, for the preference relation of the assembly as a whole (as measured by votes for each pair of measures, if each person voted their true preference) to be intransitive.

When the assembly preference relation is intransitive, then there would be a cycle if proposals could be considered more than once. If assembly preferences are intransitive and the procedure says that each proposal can only be considered once, and voters are sincere and a forward moving agenda process is used, then the agenda (the order of consideration) determines which one will win.

Theorem: the previous theorem gives a sufficient condition for a Condorcet winner; necessary conditions is given in Sen and Pattanaik (1969). These conditions are "seldom likely" to be met (Strom, chapter 2, p. 26). "See also Niemi 1983 for the effects of partially relaving the single-peakedness requirement."

Chapter 2:

When Black's theorem applies, and a committee reports a bill to a full chamber, and the full chamber is not prohibited from amending the bill, the committee has no power, because the bill will always be amended to the median peak. However, if the full chamber cannot arbitrarily amend the committee bill, but can only choose between the status quo and the reported bill, then the committee may have power.

Arrow's theorem shows that assembly transitive preferences cannot be guaranteed without accepting one of a set of seemingly undesirable properties. Plott 1976 has further discussion.

the existence of a social preference cycle does not imply that no equilibrium exists. For example, there may exist an alternative that defeats all others, but there may be cycles among the others.

In fact, when preferences are intransitive, it is possible for an proposal to win even when each individual preferred another proposal to the winner. Example; three voters, 1, 2, 3, four proposals, W,X,Y,Z. Preferences:

1: Y > X > W > Z 2: X > W > Z > Y 3: W > Z > Y > Z

Agenda: W vs X; winner vs Y; winner vs. Z. Outcome: x defeats W, Y defeats X, Z defeats Y. Z wins, even though everyone prefers W to Z.

These situations really occur; Riker 1958 discussed a case in 1953 when the U.S. House of Representatives appeared to have intransitive preferences. Blydenburgh 1971 discussed a case in 1932 when the U.S. House of Representatives appeared to have intransitive preferences.

The a priori probability of encountering intransitive assembly preferences (also called a "cyclic majority", a "paradox of voting", an "Arrow paradox") "rises rather dramatically with increases in both the number of alternatives considered and the number of voters (Niemi and Weisberg 1968; DeMayer? and Plott 1970; Gehrlein and Fishburn 1976)". Niemi and Weisberg 1968: for 3 alternatives, a priori probability of intransitivity with 3 actors is .056; with 15 actors, .082; with infinite actors, .088. If actors is held constant at 3, then with 3 alternatives: .056; with 4: .111, with 5: .16, with 6: .20. "With many actors and many alternatives, the a priori probability of a paradox can be as high as .84. This means that for a realistic number of actors and alternatives in decision-making settings such as in Congress, ... it is much more likely that a paradox will exist than it will not".

Chapter 3

"sincere voting" is when "in a choice between any two alternatives, a legislator would always vote for the alternative that he or she preferred". But sometimes it may be rational for a legislator to vote against a preferred alternative. this is called "sophisticated voting".

Example: Preferences are:

1: X > Y > Z 2: Y > Z > X 3: Z > X > Y

Agenda is: X vs. Y, winner vs. Z (from now on i'll just say: X,Y,Z). With sincere voting, Z would win. Notice that a majority prefers Y to Z. In round 1, 1 has an incentive to insincerely vote for Y instead of X, because then Y wins in the end.

McKelvey? and Niemi 1978: When series of dichotomous choices (a "binary agenda"), can represent as a decision tree where the root of the tree is the initial vote.

Black's theorem doesn't hold when some actors vote sincerely and others are sophisticated. However, if all voters are sophisticated, then Black's theorem holds. This is because all voters examine the decision tree and vote sincerely on the last vote. On the first vote (and each subsequent vote), the proposal that would be the sincere winner will always advance.

"However, when either the unidimensional or single-peaked assumption is not true," sincere and sophisticated outcomes may be different

Farquharson 1969: theorem: if binary agenda, and no voter indifferent b/t any pair of alternatives, then sophisticated voting leads to a determinate outcome.

With sophisticated voting, committees matter. For instance, if committees are allowed to block bills, then committee members may predict that the floor will amend any bill that they report on a certain topic to an alternative that they like less than the status quo. In this case they will not report a bill. This power is negative, but if there is a "closed rule" saying that bills reported by committees cannot be amended by the floor, then committees can get the floor to pass bills that it otherwise would not.

A "saving amendment" "is one that, if adopted, will allow a bill to pass which otherwise would be defeated. a "killer amendment" has the opposite effect.

Consider this example, in which the Condorcet winner is a "saving amendment"; B' is amended version of B; Q is status quo:

1: B' > Q > B 2: Q > B' > B 3: B > B' > Q

Social preference order is B' > Q > B. Should B' be called a "saving amendment"? We revise the definition to exclude this; redefine a saving amendment to be one in which (1) a majority prefers Q > B; (2) a majority prefers B' > Q; (3) a majority prefers B > B' (we're assuming that the agenda is B, B', Q). Note that this definition implies an intransitive social preference ordering. Note that the revised definition implies that a saving amendment will never pass with sincere voters. So, if a saving amendment does pass, someone must have voted insincerely.

Now consider killer amendments. Social preference order is B > Q, Q > B', B' > B. Necessarily intransitive. A killer amendment cannot pass with sophisticated voting.

So, sincere voters always pass a killer amendment and never pass a saving amendment. Sophisticated voters always pass saving amendments and never pass killer amendments (assuming complete public information on everyone's preferences).

Enelow 1981 finds an example of a saving amendment in HR 14765 in 1966, and possible example of a a killer amendment in HR 7535 in 1956. See Enelow and Koehler 1980 for more.

Why would the killer have passed if legistators are sophisticated? Some reasons: incomplete information on others' preferences (legistlators didn't realize it was a killer); or constraints on sophistication due to your constituents being mad at you if you voting against an amendment they like.

Chapter 4

When a bill is multidimensional (different components that can be amended independently, and for which legislators have different prefs), the "spatial" theory seems to me to go on to assume that potential outcomes (in this domain, bills to be passed) can be modeled as points in a metric space, and preferences can be modeled as a favorite outcomes along with a distance metric.

"Indifference curves" are sets of points where legislators don't care between the points in the set.

He says we assume that utility fns follow (1) continuity, (2) strict quasi-concavity ("the set of points preferred to or indifferent to another point is a convex set, and indifference curves are very thin"; this implies that "if X is closer to an actor's idea point than Y, then the actor prefers all points in the intervals between X and Y to Y"), (3) compactness: "the set of points preferred by an actor to a given point are closed and bounded... implies that an indifference curve can be drawn through any point, and this curve forms a boundary, making the set of points inside the curve a closed set"

So, instead of using vanilla Euclidean distance, we may want to weight some dimensions more than others (the distance curves become ellipses rather than circles). if ellipse axes are not parallel to the axes of issue dimensions, then we say the prefs are "non-separable".

Maximization of utility must find places tangent to indifference curves.

Sometimes city block distance metrics are used instead of Euclidean-ish ones. These produce indifference curves with straight lines and corners, making diamond-like shapes. Why make assumptions on the metric? (1) dont have to elicit complete cardinal preferences from voters in order to get their utilities (2) actually, many of the theorems dont make assumptions on the metric, besides continuity, strict quasi-concavity, and compactness.

For the rest of this chapter and the next two chapters we'll assume sincere voters.

If legislators have single-peaked preferences in all dimensions (i.e. their preferences are defined by an "ideal point" and distance from that point), and if their preferences are separable, and the parliamentary procedure allows division of the question, then if the question is divided into each issue dimension, and Black's theorem applies to each dimension separately. This produces the Black proposal, B. However, considered without dividing the question, B is not necessarily preferred by the majority to every other proposal.

the "win set" of a proposal, denoted W(X) for a proposal X, is the set of other proposals which would defeat X in a one-on-one majority vote.

In this case, the presence of a division of the question rule creates an equilibrium outcome where there may not be one in the absence of the rule. we call this "structurally induced equilibrium".

Theorem (Plott 1967): (in the absence of such rules) "an equilibrium outcome exists if all the ideal points of the legislators line up just right so that one legislator's ideal point is at a place at which the indifference curves from pairs of other legislators ae tangent to each other".

Feld and Grofman 1987 analyze (this result and the unlikliness of the Plott conditions?)

"Chaos Theorems" (McKelvey? 1976, 1979, Schofield (1978)): "With the exception of cases that satisfy the Platt conditions, simple majority rule in legislative decision making will be globablly intransitive". corollaries: except under Plott, no stable equilibrium exists; "if there is to be an end to voting... there is an initial motion that can guarantee that the final outcome at the end of voting will be a particular point"; "any legislator who can control the agenda... can dictate the final outcome".. the chaos theorems also suggest that predictions about "what decision a legislature will make" "cannot be made solely by knowledge of the preferences of legislators".

However, this instability does not appear to be consistent with either observational or experimental evidence. "...empirical studies like... Fenno (1996), Manley (1970), Birnbaum and Murray (1987), and many others have generally concluded... that legislative processes are stable and considerably more predictable than spatial theory allows". Riker 1958 suggests that, as strom puts it, "instability and intransitive social preference orders are not observed because the rules of Congress (and many other legislatures) limit the number of votes taken and hence do not allow intransitive social preferecne orders to be observed. In the case of three alternatives, for example, congressional rules allow for only two votes instead of the three needed to establish the existence of intransitive social preferences".

Riker 1958 identified an intransitive social preference ordering in 1953. Riker 1965 analyzed the Powell killer amendment case discussed above and concluded that the social preference ordering was intransitive, and found a 1911 case also.

Experiments: Halfpenny and Taylor 1973, Plott and Levine 1978, Krehbiel 1985.

Fiorina and Plott 1978 are the most comprehensive and detailed. When payoffs are relatively high, subjects behaved as rational actors. When low, maximized utility and were likely to select Schelling's "obvious point" (Schelling 1960 says that voters "generally select some obvious or prominent point as the group decision", e.g. (50,50) in a 100 by 100 space; "Fiorina and Plott took as the obvious point the ideal point" in the middle of the other ideal points). We restrict our attention to high payoffs. When a stable equilibrium existed, subjects tended to choose something near it. Separability of dimensions did not block this. But when no stable equilibrium existed, outcome was predictable, not chaotic. "It almost appears as if the subjects were imposing their own equilibrium close to the point at which it would theoretically be if one of the subjects had the ideal point assigned in Series 1".

"forward moving agenda process": status quo vs. proposal is first vote. "backward moving agenda process": status quo vs. proposal is last vote. "Theoretically, with a forward moving agenda process, any outcome in the whole issue space is possible, whereas a backward moving agenda process constrains the possible outcomes to those that are majority preferred to the status quo". Wilson found that the the backward moving agenda process behaved as expected (but Wilson showed that his subjects consistently voted sincerely), but that with a forward moving agenda process, the points were (only), as Strom says, "somewhat more scattered", showing that the "initial status quo [exerted] a powerful effect on the agenda" (Wilson).

So one of the predictions of the theory (chaos in the absence of Plott conditions) does not match observational or experimental results (orderliness).

Chapter 5: agenda control

[this paragraph conceptually belongs in chapter 4:]

Possible explanations:

(1) decisions tend to be unidimensional (so Black's theorem sometimes applies), (2) some voters have special power over the agenda, (3) structurally-induced stability (parliamentary rules), (4) the sincere voting assumption doesn't hold (5) some other aspect of the theory is wrong)

agenda control in congress: (1) gatekeeping power of committees; (2) optional "closed rule" in the house, which prevents amendments to bills reported by committee; (3) closed rule for bills reported by conference committee

(1): but floor has the option of discharging from committee; so the committee doesn't really have much control; also, since gatekeeping is only a negative power, can't explain "apparent success of committees in having their reported bills passed by their full chambers in largely unaltered form" (about 90%) (2): but closed rule is infrequently used, and is only in the house, not the senate; yet Fleisher and Bond (1981) showed that "the success of House and Senate committees in their respective chambers is nearly identical" (3): Shepsle and Weingast 1987 argue that this is the answer; "the membership of conference committees is made up exclusively or almost exclusively from the committees that reported the bill in eah chamber". But as Krehkiel 1987 notes (see also Bach 1984), House and Senate don't have to use conference committees on every bill; can amend a bill and send it back to other chamber; also conference committees are exceptions; Krehbiel found that 86.4% of bills passed with no conference (bayle: these %s of bills might be worthless if most bills in the count are thought unimportant). The full chamber decides whether or not to use a conference committee.

So Strom concludes that "these formal grants [of power to committees] do not appear to be very important, and they cannot explain committee success in Congress".

Informal agenda control:

Romer and Rosenthal 1978, Mackay and Weaver 1978, 1981, 1983, Denzau and Mackay 1980: agenda control in a "political failure in the agenda formation process" (Mackay and Weaver) "induced by the costs of formulating and proposing alternatives" (Strom). Thinking about alternatives, but also countering the arguments that the committee makes when they argue that they've thought about the issue more, and negotiated more, and you shouldnt destroy their hard work. Countering this entails some loss b/c some ppl will believe you're being troublesome, but also takes time b/c the committee will have arguments and data to back up their position, so you're going to have to do research and preparation to argue back.

Fenno 1966, 1973 provides some observational evidence in support of this. Fenno 1966 p. 440-41 says that "Subcommittee spokesmen defend their recommendations on the grounds that the subcommittee specialists have a more informed understanding of the subject matter than anyone else. On this basis, they appeal for a vote of confidence from their fellow members."

Fleicher and Bond 1981 show that "the single most significant factor explaining success or failure of amendments to committee bills in both chambers of Congress was the unity of the committee."

"Also consistent with the costs-of-amendments explanation of congressional committee success are the results presented by Smith 1987..... although the members of any given committee constitute less than 10 percent of the membership of the House, committee members generated about half of all floor amendments."

Another, more fundamental reason, though, is that "committees anticipate what outcomes a majority in the full chamber will accept and do not report bills that conflict in any serious way with these anticipations"

"Committee success in Congress ... does not appear to be a situation in which a committee majority forces its will on a reluctant majority.... rather, it appears that committees report bills at, or close to a position favored by a full chamber majority..."

Chapter 6: structurally inducing stability

Much of the theory has focused on forward moving agenda processes, but real legislatures use backward moving agenda processes, in which possible outcomes are restricted to the win set of the status quo (even with sophisticated voters, because such voters still vote sincerely on the last vote).

You might think that a backward moving agenda process implies "incrementalism", that is, the theory that legislatures will take the status quo and then make relatively minor adjustments to it. However, this is not implied; the win set of the status quo can include distant points.

(experimentally, however, Wilson 1986 showed that "the status quo does seem to be advantaged"; "in his backward moving agenda experiments, the status quo ... was the outcome in two out of three cases".)

"in general, the further the status quo is from the geometric center of the ideal points, the greater than number of possible outcomes and thus the greater the potential unpredictability of the outcome."

if voters have separable prefs, then under either sincere or sophisticated voting, division of the question sufficies for the median to win in each dimension (as with Black's theorem for the unidimensional case). the result for sophisticated: Kramer 1972; Denzau and Mackay 1981.

Shepsle 1979 (see also Shepsle and Weingast 1981) proposed that even without division of the question as a motion, a similar result is acheived by having bills that consider a single issue, and sending all bills on a topic to a committee for that topic.

When voters are sincere, division of the question combined with backward moving agenda process functions as expected (either the issue-wise median or the status quo will win). But with sophisticated voters, when status quo would win with sincere voting, there is no equilibrium and the outcome is indeterminant.

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