A formal framework for quantifying voter-controlled privacy

Privacy is a necessary requirement for voting. Without privacy, voters can be forced to vote in specific ways, and the forcing party can check their compliance. But offering privacy does not suffice: if a voter can reduce her privacy, an attacker can force her to do so. In this paper, we distinguish various ways that a voter can communicate with the intruder to reduce her privacy and classify them according to their ability to reduce the privacy of a voter. We develop a framework combining knowledge reasoning and trace equivalences to formally model voting protocols and define voter-controlled privacy. Our framework is quantitative, in the sense that it defines a measure for the privacy of a voter. Therefore, the framework can precisely measure the level of privacy for a voter for each of the identified privacy-reduction classes. The quantification allows our framework to capture receipts that reduce, but not nullify, the privacy of the voter.     

Ergodicity of Particle Systems

We study shift ergodicity, mixing, and related problems for invariant measures of interacting particle systems. The models we consider here include ferromagnetic stochastic Ising models, voter models, contact processes, exclusion processes, three-opinion noisy biased voter models, multi-opinion voter models, etc. Our results answer some questions for these models. One of the main techniques involved is a duality argument.     

Rationalizability and interactivity in evolutionary OLG models

We use the theory of rationalizable choices to study the survival and the extinction of types (or traits) in evolutionary OLG models. Two properties of evolutionary processes are introduced: rationalizability by a fitness ordering (i.e. only the most fit types survive) and interactivity (i.e. a withdrawal of types affects the survival of other types). Those properties are shown to be logically incompatible. We then examine whether the evolutionary processes at work in canonical evolutionary OLG models satisfy rationalizability or interactivity. We study n$n$-type version of the evolutionary OLG models of Galor and Moav (2002) and Bisin and Verdier (2001), and show that, while the evolutionary process at work in the former is generally rationalizable by a fitness ordering, the opposite is true for the latter, which exhibits, in general, interactivity.     

双随机环境下一维选举模型生存概率界的估计

本文用随机环境中随机游动的知识讨论了双随机环境中一维选举模型 ,给出了该模型生存概率界的估计 .     

Voter model in a random environment in ?d

We consider the voter model with flip rates determined by {μ_e, e ∈ E_d}, where E_d is the set of all non-oriented nearest-neighbour edges in the Euclidean lattice ?d. Suppose that {μ_e, e ∈ E_d} are independent and identically distributed (i.i.d.) random variables satisfying μ_e≥1. We prove that when d = 2, almost surely for all random environments, the voter model has only two extremal invariant measures: δ₀ and δ₁.     

A note on assessing agreement for frailty models

Assessing agreement is often of interest in biomedical sciences to evaluate the similarity of measurements produced by different raters or methods on the same subjects. We investigate the agreement structure for a class of frailty models that are commonly used for analyzing correlated survival outcomes. Conditional on the shared frailty, bivariate survival times are assumed to be independent with Weibull baseline hazard distribution. We present the analytic expressions for the concordance correlation coefficient (CCC) for several commonly used frailty distributions. Furthermore, we develop a time-dependent CCC for measuring agreement between survival times among subjects who survive beyond a specified time point. We characterize the temporal pattern in the time-dependent CCC for various frailty distributions. Our results provide a better understanding of the agreement structure implied by different frailty models.     

Voter models and external influence

ABSTRACT

In this paper, we extend the voter model (VM) and the threshold voter model (TVM) to include external influences modeled as a jump process. We study the newly-formulated models both analytically and computationally, employing diffusion approximations and mean field approximations. We derive results pertaining to the probability of reaching consensus on a particular opinion and also the expected consensus time. We find that although including an external influence leads to a faster consensus in general, this effect is more pronounced in the VM as compared to the TVM. Our findings suggest the potential importance of external influences in addition to local interactions.     

Flip Graphs of Bounded Degree Triangulations

We study flip graphs of triangulations whose maximum vertex degree is bounded by a constant k. In particular, we consider triangulations of sets of n points in convex position in the plane and prove that their flip graph is connected if and only if k > 6; the diameter of the flip graph is O(n ²). We also show that, for general point sets, flip graphs of pointed pseudo-triangulations can be disconnected for k ≤ 9, and flip graphs of triangulations can be disconnected for any k. Additionally, we consider a relaxed version of the original problem. We allow the violation of the degree bound k by a small constant. Any two triangulations with maximum degree at most k of a convex point set are connected in the flip graph by a path of length O(n log n), where every intermediate triangulation has maximum degree at most k + 4.     

A fuzzy voting scheme for hardware and software fault tolerant systems

Voting algorithms are used to arbitrate between the results of redundant modules in fault-tolerant systems. Inexact majority and weighted average voters have been used in many applications, although both have problems associated with them. Inexact majority voters require an application-specific 'voter threshold’ value to be specified, whereas weighted average voters are unable to produce a benign output when no agreement exists between the voter inputs. Neither voter type is able to cope with uncertainties associated with the voter inputs. This paper introduces a novel voting scheme based on fuzzy set theory. It softens the harsh behaviour of the inexact majority voter in the neighbourhood of the ‘voter threshold’, and handles uncertainty and some multiple error cases in the region defined by the fuzzy input variables. The voter assigns a fuzzy difference value to each pair of voter inputs based on their numerical distance. A set of fuzzy rules then determines a single fuzzy agreeability value for each individual input which describes how well it matches the other inputs. The agreeability of each voter input is then defuzzified to give a weighting value for that input which determines its contribution to the voter output. The weight values are then used in the weighted average algorithm for calculating the voter final output. The voter is experimentally evaluated from the point of view safety and availability, and compared with the inexact majority voter in a Triple Modular Redundant structured framework. The impact of changing some fuzzy variables on the performance of the voter is also investigated. We show that the fuzzy voter gives more correct outputs (higher availability) than the inexact majority voter with small and large errors, less incorrect outputs (higher safety) than the inexact majority voter in the presence of small errors, and less benign outputs than the inexact majority voter. The percentage of the benign outputs of the majority voter that are successfully handled by the fuzzy voter (resulting in correct outputs) is more than the percentage of those that are unsuccessfully resolved by the fuzzy voter (resulting in incorrect outputs). Our results suggest that the fuzzy voter is a viable alternative to a traditional inexact voter in cases where the benefits of a large increase in availability, and a considerable decrease in the number of benign outputs outweighs the cost of a small degradation in the safety performance of the system. The fuzzy voter is also a useful voting algorithm when arbitrating between the responses of dynamic channels of control systems incorporating uncertainties. This is the first reported use of a complete fuzzy voter in the context of fault tolerance.     

A stochastic investiment model for a survival conscious firm

A stochastic investiment is analyzed to show the consequences of an unwillingness by the entrepreneur to accept any positive risk of the firm's failure. The entrepreneur does not invest in additional capacity, even in the face of continuing positive expected profits, if that investment would infringe on the firm's ability to survive. Survival of the firm conditions all investment decisions, which are functions (via the physical and financial capital accounts) of the random outcomes observed at the time of decision. This conditioning shows how worse than expected outcomes will affect the firm's net asset position and its ability to survive. Managerially, the entrepreneur has principles by which to explicitly consider unpleasant surprises in planning for the continued growth of the firm. In contrast, knowledge of the random outcomes is shown to be of no consequence in an alternative model where maximization of expected profits is the sole criterion of the entrepreneur. In that model, the optimal investiment decisions can be made at the beginning of the firm's life, because those decisions are not functions of the future yields. Reduction of the survival model to a linear programming (LP) problem highlights the additional complexity of the survival problem. This reduction means that the maximum value of the objective function for the primal (expected profits) equals the minimum value of the objective function for the dual (resource costs), which economists interpret as zero profits. The zero profit consequence is in accordance with Knight's long-standing economic conjecture: If all risks are measureable, total risk aversion will result in no profits. Also, LP methods provide a way in application to analyze a wide range of risk possibilities from acceptance of no risk of failure to acceptance of some risk of failure.The economist as such does not advocate criteria of optimality. He may invent them. ... the ultimate choice is made by the procedures of decision making inherent in the institutions, laws and customs of society. Tjalling C. Koopmans, Nobel Memorial Lecture, 11th December 1975.     

The liberal paradox and the pareto set

We say that the liberal paradox occurs where the set of alternatives is a disjoint union of sets $\text{X}{}_{\mathrm{i}}$, one for each voter, if and only if the Pareto set contains no element $\text{u}$ of any $\text{X}{}_{\mathrm{i}}$ such that voter $\text{i}$ prefers $\text{u}$ to any other element of $\text{X}{}_{\mathrm{i}}$.For random profiles, we estimate the size of the Pareto set, and show that (1) if the number of voters is held fixed but the number of alternatives tends to infinity, the probability of the liberal paradox tends to 1; (2) if the number of alternatives is a fixed ratio to the number of voters and the number of voters tends to infinity, the probability of the liberal paradox tends to zero; (3) the rights can always be redistributed to the voters so that the liberal paradox does not occur; and (4) for single-peaked preferences if the sets of rights form intervals, the liberal paradox does not occur.     

Voter model in a random environment in ? d

We consider the voter model with flip rates determined by {?? _e , e ?? E _d }, where E _d is the set of all non-oriented nearest-neighbour edges in the Euclidean lattice ? ^d . Suppose that {?? _e , e ?? E _d } are independent and identically distributed (i.i.d.) random variables satisfying ?? _e ? 1. We prove that when d = 2, almost surely for all random environments, the voter model has only two extremal invariant measures: ?? ₀ and ?? ₁.     

Auctions with an asking price

This paper studies a sales mechanism, prevalent in housing markets, where the seller does not reveal or commit to a reserve price but instead publicly announces an asking price. We show that the seller sets an asking price such that, in equilibrium, buyers of certain types would accept it with positive probability. We also show that this sales mechanism, with an optimally chosen asking price set prior to the seller learning her value, does better than any standard auction with a reserve price equal to the seller’s reservation value. We then extend the analysis to the case where the asking price reveals information about the seller’s reservation value. We show that in this case there is a separating equilibrium with fully-revealing asking prices, which is revenue-equivalent to a standard auction with a reserve price set at the seller’s reservation value.     

Global bifurcations near a degenerate heterodimensional cycle

This article is devoted to investigating the bifurcations of a heterodimensional cycle with orbit flip and inclination flip, which is a highly degenerate singular cycle. We show the persistence of the heterodimensional cycle and the existence of bifurcation surfaces for the homoclinic orbits or periodic orbits. It is worthy to mention that some new features produced by the degeneracies that the coexistence of heterodimensional cycles and multiple periodic orbits are presented as well, which is different from some known results in the literature. Moreover, an example is given to illustrate our results and clear up some doubts about the existence of the system which has a heterodimensional cycle with both orbit flip and inclination flip. Our strategy is based on moving frame, the fundamental solution matrix of linear variational system is chose to be an active local coordinate system along original heterodimensional cycle, which can clearly display the non-generic properties-``orbit flip" and ``inclination flip" for some sufficiently large time.     

EFFECTS OF INDIVIDUAL HETEROGENEITY IN ESTIMATING THE PERSISTENCE OF SMALL POPULATIONS

ABSTRACT. Population viability models are commonly used to estimate the probability of persistence of small, threatened, or endangered populations. Demographic, temporal, spatial, and individual heterogeneity are important factors affecting the probability of persistence of small populations. Because stochastic process are intractable analytically (Lud-wig [1996]), computer simulation models are often used for estimating population viability via numerical techniques. Although demographic, spatial, and temporal stochasticity have been incorporated into some population viability models, individual heterogeneity has not been included. In this paper we include individual heterogeneity in a simulation model and examine probabilities of population persistence at different levels of heterogeneity and population size. Individual heterogeneity may increase the probability of persistence of small populations. The mechanism for the extension in persistence may be explained by natural selection. Genotypes persisting through a decline may be those that survive better under the conditions causing the decline. These individuals that survive and reproduce in the face of adverse conditions may extend the probability that a small population persists.     

Repeated Downsian electoral competition

We analyze an infinitely repeated version of the Downsian model of elections. The folk theorem suggests that a wide range of policy paths can be supported by subgame perfect equilibria when parties and voters are sufficiently patient. We go beyond this result by imposing several suitable refinements and by giving separate weak conditions on the patience of voters and the patience of parties under which every policy path can be supported. On the other hand, we show that only majority undominated policy paths can be supported in equilibrium for arbitrarily low voter discount factors: if the core is empty, the generic case in multiple dimensions, then voter impatience leads us back to the problem of non-existence of equilibrium. We extend this result to give conditions under which core equivalence holds for a non-trivial range of voter and party discount factors, providing a game-theoretic version of the Median Voter Theorem in a model of repeated Downsian elections. J. Duggan was supported by the National Science Foundation, grant number 0213738, is gratefully acknowledged.     

The admissible parameter space for exponential smoothing models

We discuss the admissible parameter space for some state space models, including the models that underly exponential smoothing methods. We find that the usual parameter restrictions (requiring all smoothing parameters to lie between 0 and 1) do not always lead to stable models. We also find that all seasonal exponential smoothing methods are unstable as the underlying state space models are neither reachable nor observable. This instability does not affect the forecasts, but does corrupt the state estimates. The problem can be overcome with a simple normalizing procedure. Finally we show that the admissible parameter space of a seasonal exponential smoothing model is much larger than that for a basic structural model, leading to better forecasts from the exponential smoothing model when there is a rapidly changing seasonal pattern.     

Ordering and pricing decisions in a two-echelon supply chain with asymmetric demand information

This article examines coordinated decisions in a decentralized supply chain that consists of one supplier and one retailer, and faces random demand of a single product with a short life cycle. We consider a setting where the retailer has accurate demand information while the supplier does not. Such a problem with asymmetric demand information can be viewed as an extension of the newsboy problem in which both the supplier and the retailer possess the same demand information. Combining the mechanism of sharing demand information and that of quantity discount and return policy enables us to develop three coordinated models in contrast with the basic and uncoordinated model. We are able to show the ordinal relationship among the retailer’s optimal order quantities in these four models under a general form of random demand, and compare the supply chain profits and conduct sensitivity analysis analytically in four models under uniform random demand. We also provide numerical results under normal random demand that bear a resemblance to those under uniform random demand.