Environments with semi-ordered preferences, which may exhibit indifference intransitivity, are known to allow just-noticeable differences in preference intensity to serve as interpersonally comparable units of utility. I prove two impossibility theorems for social choice in such environments....

Purpose - In 1951, Kenneth Arrow proved that it is not possible to have a group decision-making procedure that satisfies reasonable requirements like fairness. From the theoretical viewpoint, this is a great result - welldeserving the Nobel Prize that was awarded to Professor Arrow. However,...

Abstract: Since the 18th century, doubt has been raised concerning “rational” majoritarian public choice: the “voting paradox” holds, in a simple calculation made famous by the Marquis de Condorcet, that rational resolution of divergent preferences by voting is impossible. The economist...

We consider an incomplete markets international economy in discrete-time. The first result is an impossibility theorem showing that if cross-currency no-arbitrage is to hold, the exchange rate cannot be a stationary process in levels. The second result is a system of stochastic discount factor...

Two natural and potentially desirable properties for capital allocation rules are top-downconsistency and shrinking independence. Top-down consistency means that the total capital isdetermined by the aggregate portfolio risk. Shrinking independence means that the risk capitalallocated to a given...

We use a simple graphical approach to represent Social Welfare Functions that satisfy Independence of Irrelevant Alternatives and Anonymity. This approach allows us to provide simple and illustrative proofs of May's Theorem, of variants of classic impossibility results, and of a recent result on...

Judgments are the basis for almost all decisions. They often come from different models and multiple experts. This information is typically aggregated using simple averages, which leads to the well-known shared information problem. A weighted average of the individual judgments based on...

Introduction -- Elementary Logic -- Sets, Relations, Functions -- Binary Relations -- Social Choice Theoretic Framework and Arrow Impossibility Theorem -- Some Important Value-Judgments, Rules and Theorems -- Implications of Weakening of Some of Arrow Conditions -- The Method of Majority...

We consider functions that assign to each evaluation profile a preference system or a list of menu dependent preferences. The rule by which such an assignment takes place is said to be a menu dependent preference functional (MDPFL). We extend the concepts of invariance under individual cardinal...

A key part of decentralized consensus protocols is a procedure for random selection, which is the source of the majority of miners cost and wasteful energy consumption in Bitcoin. We provide a simple economic model for random selection mechanism and show that any PoW protocol with natural...

This paper analyzes the Impossibility theory of Kenneth Arrow and proposes a plausible approach to administrate this issue. The methodology which followed is based on the preferences and on the Euclidean distances. The basic idea comes from the attribute that has the middle value. Finally shows...

Bitcoin's main innovation lies in allowing a decentralized system that relies on anonymous, profit driven miners who can freely join the system. We formalize these properties in three axioms: anonymity of miners, no incentives for miners to consolidate, and no incentive to assuming multiple...

We consider an incomplete markets international economy in discrete-time. The first result is an impossibility theorem showing that if cross-currency no-arbitrage is to hold, the exchange rate cannot be a stationary process in levels. The second result is a system of stochastic discount factor...

I build a model to make a key point that social welfare functions that only rely on individual utility (or individual preference orderings) still may reflect what people typically think of as a non-welfarist approach, further suggesting that non-welfarist methods (e.g., paternalistic methods)...

In this paper we provide Impossibility Theorems for social welfare functionals. We adapt the method of proving the inevitability of dictatorial Bergson-Samuelson social welfare functions for fixed utility profiles developed in a paper by Robert P. Parks in 1976. With a little more from results...

The problem of social choice is studied on a domain with countably many individuals. In contrast to most of the existing literature which establish either non-constructive possibilities or approximate (i.e. invisible) dictators, we show that if one adds a continuity property to the usual set of...

The central formula in asset pricing relates the price of an Arrow-Debreu security to an investor's preferences and beliefs: Price of an Arrow-Debreu security = Preferences Beliefs. We observe the prices of Arrow-Debreu securities in the option markets. But we do not directly observe the extent...

The death of welfare economics has been declared several times. One of the reasons cited for these plural obituaries is that Kenneth Arrow's impossibility theorem, as set out in his path-breaking Social Choice and Individual Values in 1951, has shown that the social welfare function - one of the...

Arrow's Impossibility Theorem is commonly understood to invoke a dictatorship that is somehow lurking within our voting arrangements. A well-recognized statement of the theorem is that "any constitution that respects transitivity, independence of irrelevant alternatives and unanimity is a...

In Arrow's classical problem of demand for insurance indemnity schedules, it is well-known that the optimal insurance indemnification for an insurance buyer - or decision maker (DM) - is a deductible contract, when the insurer is a risk-neutral Expected-Utility (EU) maximizer and when the DM is...