Modeling the effect of campaign advertising on US presidential elections when differences across states matter

We provide a stochastic electoral model of the US Presidential election where candidates take differences across states into account when developing their policy platforms and advertising campaigns. Candidates understand the political and economic differences that exist across states and voters care about candidates’ policies relative to their ideals, about the frequency of candidates’ advertising messages relative to their ideal message frequency, their campaign tolerance level, and vote taking into account their perceptions of candidates’ traits and competencies with their vote also depending on their sociodemographic characteristics. In the local Nash equilibrium, candidates give maximal weight to undecided voters and swing states and little weight to committed voters and states. These endogenous weights pin down candidates’ campaign and depend on the probability with which voters choose each candidate which depends on candidates’ policies and advertising campaigns. Weights vary across candidates’ policy and ad campaigns, reflecting the importance voters in each state give to the two dimensions and the variation in voters’ preferences across states.     

Downsian Competition When No Policy is Unbeatable

This paper studies two-party electoral competition in a setting where no policy is unbeatable. It is shown that if parties take turns in choosing policy platforms and observe eachother’s choices, for one party to change position so as to win is pointless since the other party never accepts an outcome where it is sure to loose. If there is any cost to changing platform, the prediction is that the game ends in the first period with the parties converging on whatever platform the incumbent chooses. If, however, there is a slight chance of a small mistake, the incumbent does best in choosing a local equilibrium platform. This suggests that local equilibrium policies can be the predicted outcome even if the voting process is not myopic in any way.     

Government formation in a two dimensional policy space

Given any allocation of parliament seats among parties, we characterize all the stable government configurations (supported by at least a majority of the parliament) in terms of winning coalitions and policy outcomes. We consider a two dimensional policy space and we assume that there are four parties that care mainly about holding office, and only instrumentally about policy. We find that for any distribution of seats in the parliament only two scenarios are possible: either there is a party that is a member of almost all equilibrium coalitions (dominant party scenario) or there is a party that is never a member of an equilibrium coalition (dominated party scenario). We characterize the key party for each possible scenario and we show that it is sufficient that the key party has intense preferences over one the issues to guarantee the formation of a stable government coalition.     

Game theory and the french apparentements of 1951

The French apparentement electoral system is modeled as an-person cooperative game without side payments. The players are seat-maximizing political parties. Each electoral district constitutes an independent game. The Von-Neumann and Morgenstern solution is applied to generate theoretical postdictions for a cross section of observations from the 1951 French parliamentary elections. In statistical terms, this solution has a modest, but significant, degree of explanatory power.     

A consensus model of political decision-making

In this paper, a model of political consensus is introduced. Parties try to reach consensus in forming a government. A government is defined as a pair consisting of a winning coalition and a policy supported by this coalition, where a policy consists of policies on given issues. A party evaluates all governments the party belongs to with respect to some criteria. We allow the criteria to be of unequal importance to a party. These criteria concern winning coalitions and policy issues. Parties may be advised to adjust their preferences, i.e., to change their evaluation concerning some government(s) or/and the importance of the criteria, in order to obtain a better political consensus.     

Endogenous platforms: the case of many parties

We analyze existence of equilibrium in a one-dimensional model of endogenous party platforms and more than two parties. The platforms proposed by parties depend on their membership composition. The policy implemented is a function of the different proposals and the vote distribution among such proposals. It is shown that if voters are sincere there is always an equilibrium regardless of the number of parties. In the case of strategic voting behavior, existence of equilibrium can be shown provided a subadditivity condition on the outcome function holds.     

Electoral strategies in a dynamical democratic system. Geometric models

We consider a problem of Political Economics with two opposed political parties. They will attempt to capture the greatest number of voters of a discrete population of elements. It is supposed that these parties can modify in their policies to a certain degree. Our purpose is to determine the optimum position or positions for the party in terms of guaranteeing the maximum number of voters. We will apply the techniques of Computational Geometry.     

Lower bounding aggregation and direct computation for an infinite horizon one-reservoir model

We present a specialized policy iteration method for the computation of optimal and approximately optimal policies for a discrete-time model of a single reservoir whose discharges generate hydroelectric power. The model is described in (Lamond et al., 1995) and (Drouin et al., 1996), where the special structure of optimal policies is given and an approximate value iteration method is presented, using piecewise affine approximations of the optimal return functions. Here, we present a finite method for computing an optimal policy in O(n³) arithmetic operations, where n is the number of states in the associated Markov decision process, and a finite method for computing a lower bound on the optimal value function in O(m²n) where m is the number of nodes of the piecewise affine approximation.     

One-way multiparty communication lower bound for pointer jumping with applications

In this paper we study the one-way multiparty communication model, in which every party speaks exactly once in its turn. For every k, we prove a tight lower bound of Ω(n ^1/(k?1)}) on the probabilistic communication complexity of pointer jumping in a k-layered tree, where the pointers of the i-th layer reside on the forehead of the i-th party to speak. The lower bound remains nontrivial even for k = (logn)^1/2?? parties, for any constant ? > 0. Previous to our work a lower bound was known only for k =3 (Wigderson, see [7]), and in restricted models for k>3 [2},24,18,4,13]. Our results have the following consequences to other models and problems, extending previous work in several directions. The one-way model is strong enough to capture general (not one-way) multiparty protocols with a bounded number of rounds. Thus we generalize two problem areas previously studied in the 2-party model (cf. [30,21,29]). The first is a rounds hierarchy: we give an exponential separation between the power of r and 2r rounds in general probabilistic k-party protocols, for any k and r. The second is the relative power of determinism and nondeterminism: we prove an exponential separation between nondeterministic and deterministic communication complexity for general k-party protocols with r rounds, for any k,r. The pointer jumping function is weak enough to be a special case of the well-studied disjointness function. Thus we obtain a lower bound of Ω(n ^1/(k?1)) on the probabilistic complexity of k-set disjointness in the one-way model, which was known only for k = 3 parties. Our result also extends a similar lower bound for the weaker simultaneous model, in which parties simultaneously send one message to a referee [12]. Finally, we infer an exponential separation between the power of any two different orders in which parties send messages in the one-way model, for every k. Previous results [29, 7] separated orders based on who speaks first. Our lower bound technique, which handles functions of high discrepancy over cylinder intersections, provides a “party-elimination” induction, based on a restricted form of a direct-product result, specific to the pointer jumping function.     

Downsian competition with four parties

Our purpose in this article is to study a unidimensional model of spatial electoral competition with four political parties. We assume that the voters are distributed along [0,1] in such a way that the density δ of this distribution is continuous on [0,1] and strictly positive on (0,1). The parties engage in a Downsian competition which is modeled as a non-cooperative four-person game with [0,1] as the common strategy set. If ξ_i stands for the ith quartile of the above-mentioned distribution, then we prove that has a pure Nash equilibrium, if and only if for every t (ξ₁,ξ₃). Moreover, if this condition is satisfied, then has exactly six pure Nash equilibria, which are characterized by the fact that two of the parties put forward the policy that corresponds to ξ₁ and the other two of them put forward the policy that corresponds to ξ₃.     

Asymptotic bias of some election methods

Consider an election where N seats are distributed among parties with proportions p ₁,…,p _m of the votes. We study, for the common divisor and quota methods, the asymptotic distribution, and in particular the mean, of the seat excess of a party, i.e. the difference between the number of seats given to the party and the (real) number Np _i that yields exact proportionality. Our approach is to keep p ₁,…,p _m fixed and let N→∞, with N random in a suitable way. In particular, we give formulas showing the bias favouring large or small parties for the different election methods.     

Optimal allocation of policy limits and deductibles in a model with mixture risks and discount factors

By maximizing the expected utility, we study the optimal allocation of policy limits and deductibles from the viewpoint of a policyholder, where the dependence structure of losses is unknown. In Cheung (2007) [K.C. Cheung, Optimal allocation of policy limits and deductibles, Insurance: Mathematics and Economics 41 (2007) 382-391], the author had considered similar problems. He supposed that a policyholder was exposed to n random losses, and the losses were general risks there, i.e., the loss on each policy was just a random variable. In this paper, the model is extended in two directions. On one hand, we assume that n policies of the n losses are effected by random environments. For each policy, the loss under a fixed environment is characterized by a random variable, so the loss on each policy is a mixture of some fundamental random variables. On the other hand, loss frequencies, which are stochastic, are also considered. Therefore, the whole model is equipped with mixture risks and discount factors. Finally, we get the orderings of the optimal allocations of policy limits and deductibles. Our conclusions also extend the main results in Hua and Cheung (2008) [L. Hua, K.C. Cheung, Stochastic orders of scalar products with applications, Insurance: Mathematics and Economics 42 (2008) 865-872].     

On optimal right-of-way policies at a single-server station when insertion of idle times is permitted

A general stream of n types of customers arrives at a Single Server station where service is non-preemptive, the server may undergo Poisson breakdowns and insertion of idle times is allowed. If ξ(k) and c(k) are, respectively, the expected service time and sojourn cost per unit time of a type k customer (1?k?n), call k “V.I.P.” type if ξ(k)/c(k) = min_1?i?n[ξ(i)/sbc(i)].We show that any right-of-way service policy can be improved by a policy that grants V.I.P. customers priority over all others, and never inserts idle time when a V.I.P. customer is present.We further show that if the arrival stream is Poisson, the so-called “cμ” priority rule (applied with no delays) is optimal in the class of all service policies, and not just among those of a priority nature.     

Intra-party decision making, party formation, and moderation in multiparty systems

We establish coalitional stable party structures of a party formation game in an elected assembly. Farsighted political players can commit to form parties and to vote on policies according to the party position which is determined by intra-party majority rule. Parties may form governments and block proposals by a randomly selected member of the government. If the government recognition rule allows for the formation of multiparty governments, the median parliamentarian either realizes her ideal point or a policy lottery which she strictly prefers to the status quo. This outcome is enforced by the threat of forming a moderating centre party.     

Policy and the standards debate: mapping changes in assessment in mathematics

ABSTRACT

The influences on governments for policy changes in schools range across many agencies, including the political party in power. When policies change, the sources of these influences are not always clear. The project whose work is presented in this special issue examines what these changes look like in terms of the differences in assessment tasks of school pupils’ mathematics, over time. In this article we attempt to develop a graph, which we argue will have general applicability internationally, that can help to reveal the sources and nature of those influences. We construct the graph in interaction with an examination of the most recent changes in two countries. We argue that our analysis is a necessary complement to the project’s findings in that it enables us to identify the fields of recontextualisation, their relative strengths in terms of influence and hence conjecture their impact on the mathematics curriculum.     

Optimal and near-optimal policies for lost sales inventory models with at most one replenishment order outstanding

In this paper we use policy-iteration to explore the behaviour of optimal control policies for lost sales inventory models with the constraint that not more than one replenishment order may be outstanding at any time. Continuous and periodic review, fixed and variable lead times, replenishment order sizes which are constrained to be an integral multiple of some fixed unit of transfer and service level constraint models are all considered. Demand is discrete and, for continuous review, assumed to derive from a compound Poisson process. It is demonstrated that, in general, neither the best (s, S) nor the best (r, Q) policy is optimal but that the best policy from within those classes will have a cost which is generally close to that of the optimal policy obtained by policy iteration. Finally, near-optimal computationally-efficient control procedures for finding (s, S) and (r, Q) policies are proposed and their performance illustrated.     

Local Nash Equilibrium in Multiparty Politics

We present a model of multi-party, spatial competition under proportional rule with both electoral and coalitional risk. Each party consists of a set of delegates with heterogeneous policy preferences. These delegates choose one delegate as leader or agent. This agent announces the policy declaration (or manifesto) to the electorate prior to the election. The choice of the agent by each party elite is assumed to be a local Nash equilibrium to a game form . This game form encapsulates beliefs of the party elite about the nature of both electoral risk and the post-election coalition bargaining game. It is demonstrated, under the assumption that is smooth, that, for almost all parameter values, a locally isolated, local Nash equilibrium exists.In the final section of the paper some empirical work is reviewed in order to obtain some insights into why parties do not simply converge to an electoral center in order to maximize expected vote shares.     

Managing the order pipeline to reduce supply chain volatility

The bullwhip effect in particular, and supply chain volatility in general, has been the subject of much analytical and empirical investigation by researchers. One goal of this work has been to determine supply chain designs and policies that minimize volatility. Using a system dynamics approach, we use three distinct supply chain volatility metrics to compare the ability of two alternative pipeline inventory management policies to respond to a demand shock. The results indicate that no one policy dominates on all three metrics of supply chain volatility. A simplistic static pipeline policy minimizes the bullwhip effect and lessens the likelihood of on-hand inventory oscillations, while a more sophisticated dynamic pipeline policy may converge more rapidly to the new equilibrium. In addition, simulation results suggest that the dynamic policy provides better customer service through fewer stockouts and backorders.     

The General Problem of <Emphasis Type="Italic">m</Emphasis> Persons and <Emphasis Type="Italic">n</Emphasis> Positions for Short- and Long-Term Decision-Making

This paper discusses the well-known problems of m candidates and n positions usually called term assignment problems. The paper considers these problems when decisions for short and long term policies must be taken and also in extreme situations, such as emergency cases. Assignment and Knapsack problems, Heirarchy Analysis, Graphs Theory and Metric Spaces using Dynamic Programming are used on a computer.     

The give-up problem for blocked regional lists with multi-winners

The current electoral law for the Italian Parliament prescribes blocked, linearly ordered lists of candidates for each party within each constituency. The peculiarity of the Italian electoral system is that a party can present the same candidate in different constituencies. There are several seats at stake in each constituency; these seats are allocated to the parties proportionally to the total number of votes they get. If the blocked list mechanism-which assigns the seats obtained by a party in a constituency to the first candidates of the corresponding ordered list-causes some candidates to win in more than one constituency, they may retain only one of the seats, giving up all the remaining ones. Thus, the problem arises for a party to find a suitable “schedule of give-ups” that produces the final set of winners for that party. In order to do this, we assume that such decision is centralized and based on some models of global (inter-regional) preferences over the set of candidates. In this paper, we introduce two classes of models to formulate the “give-up problem”, i.e., utility and ordinal models, and we show that for both of them some natural formulations of the problem can be efficiently solved by network flows techniques.