Steven J Bram
Biographic Data
| ID | 350026 |
|---|---|
| NAME | Steven J Bram |
| GIVEN NAMES | Steven J |
| FAMILY NAME | Bram |
| SIGNATURE | BRAM S J |
| AFFILIATIONS | New York University |
| ORCID | 0000-0003-3650-0392 |
| VERIFIED | Yes |
| TOTAL WORKS | 107 |
| TOTAL CITATIONS | 670 |
| AUTHOR COUNT | 107 |
| EDITOR COUNT | 0 |
| FIRST PUBLICATION YEAR | 1966 |
| LATEST PUBLICATION YEAR | 2026 |
| H-INDEX | 12 |
Preventing gerrymandering: A moving-knife algorithm to draw congressional districts
To prevent gerrymandering of U.S. House of Representative districts, we describe and apply a computationally feasible moving-knife algorithm (MKA) to draw congressional districts that are nonpartisan and compact. MKA maximizes a measure of geographic compactness that precludes political parties from influencing the drawing of district boundaries. MKA begins by constructing the “minimum bounding circle” of a state, which encircles it as tightly as…
Two-Person Fair Division of Indivisible Items: Bentham vs. Rawls on Envy
Suppose two players wish to divide a finite set of indivisible items, over which each distributes a specified number of points. Assuming the utility of a player’s bundle is the sum of the points it assigns to the items it contains, we analyze what divisions are fair. We show that if there is an envy-free (EF) allocation of the items, two other desirable properties—Pareto-optimality (PO) and Maximinality (MM)—can also be satisfied, rendering these…
The excess method: A multiwinner approval voting procedure to allocate wasted votes
Peter C. Fishburn (1936–2021)
Every normal-form game has a Pareto-optimal nonmyopic equilibrium
It is well known that Nash equilibria may not be Pareto-optimal; worse, a unique Nash equilibrium may be Pareto-dominated, as in Prisoners’ Dilemma. By contrast, we prove a previously conjectured result: every finite normal-form game of complete information and common knowledge has at least one Pareto-optimal nonmyopic equilibrium (NME) in pure strategies, which we define and illustrate. The outcome it gives, which depends on where play starts, m…
Peter C. Fishburn (1936–2021)
Peter C. Fishburn (1936–2021)
Making Partisan Gerrymandering Fair: One Old and Two New Methods
Objective To introduce a novel way to make partisan gerrymandering fair. Methods In the context of two parties, divide a state into two geographical areas, each of which contain a number of districts that are roughly proportional to the share of the statewide vote received by each party in the last congressional elections. Allow each party to unilaterally design the districts in a designated area of the state, restricted only by traditional distr…
Multiwinner approval voting: An apportionment approach
Divine Games: Game Theory and the Undecidability of a Superior Being
A game-theoretical analysis of interactions between a human being and an omnipotent and omniscient godlike being highlights the inherent unknowability of the latter's superiority. In Divine Games, Steven Brams analyzes games that a human being might play with an omnipotent and omniscient godlike being. Drawing on game theory and his own theory of moves, Brams combines the analysis of thorny theological questions, suggested by Pascal's wager (whic…
Books By Our Readers
An abstract is not available for this content. As you have access to this content, full HTML content is provided on this page. A PDF of this content is also available in through the ‘Save PDF’ action button
Paths to victory in presidential elections: The setup power of noncompetitive states
How to Divide Things Fairly
We propose an intuitively simple sequential algorithm (SA) for the fair division of indivisible items that are strictly ranked by two or more players. We analyze several properties of the allocations that it yields and discuss SA's application to real-life problems, such as dividing the marital property in a divorce or assigning people to committees or projects. Additional informationNotes on contributorsSteven J. BramsSTEVEN J. BRAMS (MR Author …
The paradox of grading systems
Coalition formation on the U.S. Supreme Court: 1969–2009
Narrowing the field in elections: The Next-Two rule
We suggest a new approach to narrowing the field in elections, based on the ‘deservingness’ of candidates to be contenders in a runoff, or to be declared one of several winners. Instead of specifying some minimum percentage (e.g., 50) that the leading candidate must surpass to avoid a runoff (usually between the top two candidates), we propose that the number of contenders depends on the distribution of votes among all candidates. Divisor methods…
Game Theory and the Humanities: Bridging Two Worlds
How game theory can offer insights into literary, historical, and philosophical texts ranging from Macbeth to Supreme Court decisions. Game theory models are ubiquitous in economics, common in political science, and increasingly used in psychology and sociology; in evolutionary biology, they offer compelling explanations for competition in nature. But game theory has been only sporadically applied to the humanities; indeed, we almost never associ…
A note on the inefficiency of bidding over the price of a share
Fair Division
This article provides a review of the literature on fair division, which has flourished in recent years. It focuses on three different literatures in the field: the allocation of several indivisible goods, the division of a single heterogeneous good, and the division, in whole or in part, of several divisible goods. The article discusses problems that arise in allocating indivisible goods, and highlights the trade-offs that must be made when not …
A minimax procedure for electing committees
Scheduling of panels by integer programming: Results for the 2005 and 2006 New Orleans meetings
Influence in Terrorist Networks: From Undirected to Directed Graphs
A methodology for converting terrorist networks from undirected graphs to simplified directed graphs (or digraphs), and mapping the flow of influence in them, is described. It is based on an “influence assumption”—that important persons with more links influence less important persons with fewer links. This methodology, which was previously used to analyze the structure of influence relationships in Communist-bloc countries and the international …
The normative turn in public choice
Dead Heat: The 2006 Public Choice Society Election
Critical strategies under approval voting: Who gets ruled in and ruled out
Approval Voting
Approval voting is a method of voting in which voters can vote for ("approve of") as many candidates as they wish in an election. This article analyzes properties of this method and compares it with other single-ballot nonranked voting systems. Among the theorems proved is that approval voting is the most sincere and most strategyproof of all such voting systems; in addition, it is the only system that ensures the choice of a Condorcet majority c…
Transaction Flows in the International System
When we speak of aninternational system, we start with the presumption that there is something habitual and regular about the behavior of the nations that constitute it. Unfortunately, the concept of an international system has had a singularly hollow ring in the works of many scholars who have employed the term. It is frequently compared to an incredibly complicated watch or thermostat, or alternatively it is defined so abstractly that it would …
The 3/2's Rule in Presidential Campaigning
The purpose of this article is to assess the effect of the winner-take-all feature of the Electoral College on the allocation of resources by candidates to the states in a presidential campaign. Conceptualizing the campaign as a two-person zero-sum infinite game, it is found that the main effect of this feature is to induce candidates to allocate campaign resources roughly in proportion to the 3/2's power of the electoral votes of each state, whi…
The Paradox of Vote Trading
Although, conventionally, vote trading in legislatures has been condemned as socially undesirable by both scholars and lay citizens, a recently popular school of scholarship has argued that vote trading improves the traders' welfare in the direction of Pareto-optimal allocations. This essay is an attempt to reconcile the disagreement by showing formally that vote trading does improve the position of the traders but that at the same time trading m…
Patterns of Representation in National Capitals and Intergovernmental Organizations
Although the first recorded permanent diplomatic mission was established by the Duke of Milan at Genoa over five hundred years ago, knowledge of the structure and functioning of the global diplomatic enterprise is still extremely limited. The often-cited work of Nicolson provides a historical overview of diplomacy, describes some of the norms of recent practice, and enumerates traits of “the ideal diplomatist.” Morgenthau has analyzed the importa…
New paradoxes of voting power on the EC Council of Ministers
Threat Escalation and Crisis Stability: A Game-theoretic Analysis
We develop a model of crisis stability based on a deterrence game. Players are assumed to be able to choose any level of initial cooperation or noncooperation; the more cooperative player (if there is one) may then choose to retaliate. In a crisis, players are assumed to have escalated their conflict and desire to stabilize it before it explodes. Players can, by threatening their opponent, stabilize the new status quo. In addition, points of thre…
Nonmyopic Equilibria in 2×2 Games
Measuring the Concentration of Power in Political Systems
The unequal distribution of power among the members of a political system is one of the most pervasive facts of political life. Yet, while many studies have confirmed the fact that a few members exercise disproportionate control over many others in most systems, the configurations of power relations that occur among the few have generally not been subjected to systematic comparative analysis. In a few notable empirical studies, attempts have been…
The Geometry of the Arms Race
This article develops a new methodology for analyzing the arms race between the two superpowers based on an extension of the classic Prisoner's Dilemma game to allow for sequences of moves. The sequence that is formally analyzed depends on a scenario in which each side: (1) possesses an ability to detect what the other side is doing with a specified probability, and (2) pursues a tit-for-tat policy of conditional cooperation—i.e., cooperates if i…
Voting on referenda: The Separability Problem and Possible Solutions
Assume that voters choose between yes (Y) and no (N) on two related propositions in a referendum, where YN, for example, signifies voting Y on the first and N on the second. If a voter's preference order for the four possible combinations is, say, YY>NN>YN>NY, then this voter's preferences are nonseparable, because whether he or she will prefer Y or N on either proposition depends on whether Y or N is the outcome selected on the other. Since vote…
Newcomb's Problem and Prisoners' Dilemma
The relationship between Newcomb's problem, which involves an apparent paradox of prediction, and Prisoners' Dilemma is explicated. After describing a resolution to Newcomb's problem, due to John A. Ferejohn, that renders the two contradictory principles of choice in Newcomb's problem (dominance and expected utility) consistent, I show Prisoners' Dilemma to be a “symmetricized” version of Newcomb's problem in its payoff structure. The assumption …
Threat Power in Sequential Games
The analysis of 2 × 2 ordinal games, in which both players can sequentially move and countermove after an initial outcome is chosen, is extended to repeated play of these games in which one player has ‘threat power’. This power enables this player to threaten the other player with a mutually disadvantageous outcome in order to deter certain moves in the future play of the game. Except for no-conflict games with a mutually best outcome, there are …
Proportional Representation: Broadening the Options
Using a recent article by Monroe as a springboard, we extend and generalize his system of proportional representation (PR) by developing a general method for determining a set of winners from the ballots. Central to our analysis is the use of integer programming, which is a type of linear programming. Under Monroe's system and our generalizations of it, one minimizes total misrepresentation, where misrepresentation is based on approval votes, the…
Game Theory and the Humanities: Bridging Two Worlds
How game theory can offer insights into literary, historical, and philosophical texts ranging from Macbeth to Supreme Court decisions. Game theory models are ubiquitous in economics, common in political science, and increasingly used in psychology and sociology; in evolutionary biology, they offer compelling explanations for competition in nature. But game theory has been only sporadically applied to the humanities; indeed, we almost never associ…
Dividing the Indivisible: Procedures for Allocating Cabinet Ministries to Political Parties in a Parliamentary System
Political parties in Northern Ireland recently used a divisor method of apportionment to choose, in sequence, ten cabinet ministries. If the parties have complete information about each other’s preferences, we show that it may not be rational for them to act sincerely by choosing their most-preferred ministry that is available. One consequence of acting sophisticatedly is that the resulting allocation may not be Pareto-optimal, making all the par…
An Axiomatic Model of Voting Bodies
The act of voting in legislative and judicial bodies is one of the most widespread and valuable sources of information available to political analysts. When individuals make structured choices within some known institutional constraints, there is opportunity for the generation of data concerning how issues are collectively defined within an institution, the relative position of each actor with regard to every other actor, and the identification o…
Single-Peakedness and Disconnected Coalitions
Ordinally single-peaked preferences are distinguished from cardinally single-peaked preferences, in which all players have a similar perception of distances in some one-dimensional ordering. While ordinal single-peakedness can lead to disconnected coalitions that have a ‘hole’ in the ordering, cardinal single-peakedness precludes this possibility, based on two models of coalition formation: • Fallback (FB): Players seek coalition partners by desc…
The responsiveness of approval voting: Comments on Saari and Van Newenhizen
Winding Down if Preemption or Escalation Occurs: A Game-Theoretic Analysis
Game-theoretic models of deterrence and escalation, based on Chicken and Prisoners' Dilemma, are developed in which two players can initially choose any level of preemption in a crisis (Deterrence Game) or escalation in an arms race (Deescalation Game). The greater this level, the more likely an opponent will interpret this choice as a noncooperative action and retaliate. Given that both players make noncooperative choices in these games—either i…
Deterrence versus Defense: A Game-Theoretic Model of Star Wars
A game-theoretic model of the Strategic Defense Initiative, or "Star Wars," is developed based on a deterrence model founded on the game of Chicken. In this model, two players can choose any level of preemption, and threaten any level of retaliation against preemption, whereas in the Star Wars Game they are constrained in these choices by the defensive capabilities of an opponent. Nash equilibria, or stable outcomes, are derived in this game and …
Manipulability of voting by sincere truncation of preferences
Optimal resource allocation in presidential primaries
Strategic information and voting behavior
Game Theory and Emotions
To illustrate the rational-choice modeling of emotions, a game-theoretic model of frustration, in which players respond in anger to their lack of control, is developed. Of the 57 distinct 2 × 2 strict ordinal conflict games, 12 turn out to be `frustration games', in four of which `threat power', based on the theory of moves, offers relief to the frustrated player. Aristophanes' play, Lysistrata, in which the frustrated women induce the men to sto…
Transaction Flows in the International System
When we speak of aninternational system, we start with the presumption that there is something habitual and regular about the behavior of the nations that constitute it. Unfortunately, the concept of an international system has had a singularly hollow ring in the works of many scholars who have employed the term. It is frequently compared to an incredibly complicated watch or thermostat, or alternatively it is defined so abstractly that it would …
Patterns of Representation in National Capitals and Intergovernmental Organizations
Although the first recorded permanent diplomatic mission was established by the Duke of Milan at Genoa over five hundred years ago, knowledge of the structure and functioning of the global diplomatic enterprise is still extremely limited. The often-cited work of Nicolson provides a historical overview of diplomacy, describes some of the norms of recent practice, and enumerates traits of “the ideal diplomatist.” Morgenthau has analyzed the importa…
A Note On the Cosmopolitanism of World Regions
Measuring the Concentration of Power in Political Systems
The unequal distribution of power among the members of a political system is one of the most pervasive facts of political life. Yet, while many studies have confirmed the fact that a few members exercise disproportionate control over many others in most systems, the configurations of power relations that occur among the few have generally not been subjected to systematic comparative analysis. In a few notable empirical studies, attempts have been…
The Search for Structural Order in the International System: Some Models and Preliminary Results
Journal Article The Search for Structural Order in the International System: Some Models and Preliminary Results Get access Steven J. Brams Steven J. Brams New York University Search for other works by this author on: Oxford Academic Google Scholar International Studies Quarterly, Volume 13, Issue 3, September 1969, Pages 254–280, https://doi.org/10.2307/3013531 Published: 01 September 1969
The Apsa and Minority Representation
The concept of representation has been much discussed and debated in the literature of political science. My intent here is not to review or evaluate the different meanings or implications that have been given to this concept but instead to focus on specific voting schemes which would allow the expression of minority (as well as majority) viewpoints in an elected voting body in rough proportion to their numbers of supporters in a larger electorat…
An Axiomatic Model of Voting Bodies
The act of voting in legislative and judicial bodies is one of the most widespread and valuable sources of information available to political analysts. When individuals make structured choices within some known institutional constraints, there is opportunity for the generation of data concerning how issues are collectively defined within an institution, the relative position of each actor with regard to every other actor, and the identification o…
Comment on Mayer's “A Note on ‘An Axiomatic Model of Voting Bodies’”
An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
The Paradox of Vote Trading
Although, conventionally, vote trading in legislatures has been condemned as socially undesirable by both scholars and lay citizens, a recently popular school of scholarship has argued that vote trading improves the traders' welfare in the direction of Pareto-optimal allocations. This essay is an attempt to reconcile the disagreement by showing formally that vote trading does improve the position of the traders but that at the same time trading m…
When to join a coalition, and with how many others, depends on what you expect the outcome to be
The 3/2's Rule in Presidential Campaigning
The purpose of this article is to assess the effect of the winner-take-all feature of the Electoral College on the allocation of resources by candidates to the states in a presidential campaign. Conceptualizing the campaign as a two-person zero-sum infinite game, it is found that the main effect of this feature is to induce candidates to allocate campaign resources roughly in proportion to the 3/2's power of the electoral votes of each state, whi…
Newcomb's Problem and Prisoners' Dilemma
The relationship between Newcomb's problem, which involves an apparent paradox of prediction, and Prisoners' Dilemma is explicated. After describing a resolution to Newcomb's problem, due to John A. Ferejohn, that renders the two contradictory principles of choice in Newcomb's problem (dominance and expected utility) consistent, I show Prisoners' Dilemma to be a “symmetricized” version of Newcomb's problem in its payoff structure. The assumption …
Bandwagons in Coalition Formation: The 2/3's Rule
"Comment on "Campaign Resource Allocations under the Electoral College
An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content
Unanimity in the supreme court: A game-theoretic explanation of the decision in the white house tapes case
Deception in simple voting games
Another Solution
An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content
Approval Voting
Approval voting is a method of voting in which voters can vote for ("approve of") as many candidates as they wish in an election. This article analyzes properties of this method and compares it with other single-ballot nonranked voting systems. Among the theorems proved is that approval voting is the most sincere and most strategyproof of all such voting systems; in addition, it is the only system that ensures the choice of a Condorcet majority c…
Resource Allocations in the 1976 Campaign
An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content
Applied Game Theory
Replies
An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content
The Geometry of the Arms Race
This article develops a new methodology for analyzing the arms race between the two superpowers based on an extension of the classic Prisoner's Dilemma game to allow for sequences of moves. The sequence that is formally analyzed depends on a scenario in which each side: (1) possesses an ability to detect what the other side is doing with a specified probability, and (2) pursues a tit-for-tat policy of conditional cooperation—i.e., cooperates if i…
Approval Voting in Multicandidate Elections
Nonmyopic Equilibria in 2×2 Games
Efficacy, power and equity under approval voting
Political science (81 works) · Law (74 works) · Economics (69 works) · Law (58 works) · Computer Science (56 works) · Politics (46 works) · Mathematics (42 works) · Mathematical economics (39 works) · Game Theory and Voting Systems (37 works) · Law and economics (31 works)