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In this paper we consider decision functions in which voters have three options and one of them is abstention or indifference and the output is a binary decision between two alternatives so that a tie is not possible. These resolute decision functions appear frequently in grading, in some sport competitions, in voting situations in which the status quo is put to the vote, etc. It is a more restricted case of the voting context considered in the seminal article by Kenneth May on decision functions, published in Econometrica in 1952, because the output set does not admit a tie. Among these resolute decision functions we focus on the study of majority functions, in which the number of favorable votes to an alternative must be strictly greater than the number of votes against it. This work provides an axiomatic characterization for the set of majority functions and for the relative majority function with status quo bias. Both characterizations are based on weaker versions of neutrality. Other complementary characterizations are also provided.

We study the Galam majority rule dynamics with contrarian behavior and an oscillating external propaganda in a population of agents that can adopt one of two possible opinions. In an iteration step, a random agent interacts with three other random agents and takes the majority opinion among the agents with probability p(t) (majority behavior) or the opposite opinion with probability 1−p(t) (contrarian behavior). The probability of following the majority rule p(t) varies with the temperature T and is coupled to a time-dependent oscillating field that mimics a mass media propaganda, in a way that agents are more likely to adopt the majority opinion when it is aligned with the sign of the field. We investigate the dynamics of this model on a complete graph and find various regimes as T is varied. A transition temperature Tc separates a bimodal oscillatory regime for TTc in which m oscillates around zero. These regimes are characterized by the distribution of residence times that exhibit a unique peak for a resonance temperature T*, where the response of the system is maximum. An insight into these results is given by a mean-field approach, which also shows that T* and Tc are closely related.

I address the challenge of extracting reliable insights from large datasets using a simplified model that illustrates how hierarchical classification can distort outcomes. The model consists of discrete pixels labeled red, blue, or white. Red and blue indicate distinct properties, while white represents unclassified or ambiguous data. A macro-color is assigned only if one color holds a strict majority among the pixels. Otherwise, the aggregate is labeled white, reflecting uncertainty. This setup mimics a percolation threshold at fifty percent. Assuming that directly accessing the various proportions from the data of colors is infeasible, I implement a hierarchical coarse-graining procedure. Elements (first pixels, then aggregates) are recursively grouped and reclassified via local majority rules, ultimately producing a single super-aggregate for which the color represents the inferred macro-property of the collection of pixels as a whole. Analytical results supported by simulations show that the process introduces additional white aggregates beyond white pixels, which could be present initially; these arise from groups lacking a clear majority, requiring arbitrary symmetry-breaking decisions to attribute a color to them. While each local resolution may appear minor and inconsequential, their repetitions introduce a growing systematic bias. Even with complete data, unavoidable asymmetries in local rules are shown to skew outcomes. This study highlights a critical limitation of recursive data reduction. Insight extraction is shaped not only by data quality but also by how local ambiguity is handled, resulting in built-in biases. Thus, the related flaws are not due to the data but to structural choices made during local aggregations. Although based on a simple model, these findings expose a high likelihood of inherent flaws in widely used hierarchical classification techniques.

Democracy is upheld through the principle of majority rule. To validate the application of democracy, it is imperative to assess the sincerity of voter decisions. When voter sincerity is compromised, manipulation may occur, thereby undermining the legitimacy of democratic processes. This paper presents a general version of a symmetric dichotomous choice model. Using simple majority rule, we show that when a voter receives one or more private signals, sincere voting is an equilibrium behavior. A slight change to this basic model may create an incentive to vote insincerely. We show that even in a more restricted model where every voter receives only one private signal whose level of precision is the same for all the voters but depends on the state of nature, voters may have an incentive to vote insincerely.

In German federal elections, district representatives are chosen by plurality rule – a voting system that can fail to select the Condorcet winner. With heightened party system fragmentation, violations of the Condorcet criterion may become increasingly frequent. In light of the »horseshoe theory«, it also becomes questionable whether Condorcet winners exist in the first place. In this study, we simulate preference orderings over district candidates for the 2017 Bundestag election based on survey data. The simulation identifies Condorcet winners in every district and indicates that plurality rule fails to select those in about one in ten districts.

We characterize the voluntary public service policy that minimizes the expected cost of delivering a public service (e.g., jury or military service). We then examine whether a majority rule voting procedure will implement the voluntary public service policy (VPS) whenever it entails lower expected cost than mandatory public service (MPS). We find that majority rule often favors MPS in the sense that majority rule implements MPS when VPS would secure the requisite public service at lower expected cost.

We define the class of two-player zero-sum games with payoffs having mild discontinuities, which in applications typically stem from how ties are resolved. For such games, we establish sufficient conditions for existence of a value of the game, maximin and minimax strategies for the players, and a Nash equilibrium. If all discontinuities favor one player, then a value exists and that player has a maximin strategy. A property called payoff approachability implies existence of an equilibrium, and that the resulting value is invariant: games with the same payoffs at points of continuity have the same value and ε-equilibria. For voting games in which two candidates propose policies and a candidate wins election if a weighted majority of voters prefer his proposed policy, we provide tie-breaking rules and assumptions about voters' preferences sufficient to imply payoff approachability. These assumptions are satisfied by generic preferences if the dimension of the space of policies exceeds the number of voters; or with no dimensional restriction, if the electorate is sufficiently large. Each Colonel Blotto game is a special case in which each candidate allocates a resource among several constituencies and a candidate gets votes from those allocated more than his opponent offers; in this case, for simple-majority rule we prove existence of an equilibrium with zero probability of ties.

Under the unanimity rule, a single voter may alter a decision that is unanimously accepted by all other voters. Under the simple majority rule, the impact of such a voter diminishes. This paper examines the marginal effect of competence on the collective performance—the likelihood of reaching a correct decision. It is shown that adding an incompetent voter to the group is inferior (superior) to giving up an existing competent voter, when the decision mechanism is the unanimity (simple majority) rule. The negative impact of an incompetent voter cannot (can) always be balanced by adding a competent one under the unanimity (simple majority) rule. Moreover, improving a single voter’s competence may have a greater effect on the collective performance under the simple majority rule relative to the unanimity rule.

I introduce a model of shareholder voting. I describe and provide characterizations of three families of shareholder voting rules: ratio rules, difference rules, and share majority rules. The characterizations rely on two key axioms: merger consistency, which requires consistency in voting outcomes following stock-for-stock mergers, and reallocation invariance, which requires the shareholder voting rule to be immune to certain manipulative techniques used by shareholders to hide their ownership. The paper also extends May's theorem.

Political scientists frequently interpret the results of conjoint experiments as reflective of majority preferences. In this article, we show that the target estimand of conjoint experiments, the average marginal component effect (AMCE), is not well defined in these terms. Even with individually rational experimental subjects, the AMCE can indicate the opposite of the true preference of the majority. To show this, we characterize the preference aggregation rule implied by the AMCE and demonstrate its several undesirable properties. With this result, we provide a method for placing bounds on the proportion of experimental subjects who prefer a given candidate feature. We describe conditions under which the AMCE corresponds in sign with the majority preference. Finally, we offer a structural interpretation of the AMCE and highlight that the problem we describe persists even when a model of voting is imposed.