Tootfinder

Plenitudinous Urelements and the Definability of Cardinality
Bokai Yao
https://arxiv.org/abs/2508.20641 https://arxiv.org/pdf/2508.20641

Plenitudinous Urelements and the Definability of Cardinality
The Axiom of Plenitude asserts that every ordinal is equinumerous with a set of urelements, while its stronger form, Plenitude$^+$, extends it to all sets. We investigate these two axioms within ZF set theory with urelements. Assuming that cardinality is definable, Plenitude$^+$ unifies the Collection Principle and the Reflection Principle, which are otherwise conjectured to be non-equivalent. If either cardinality is representable or the principle of Small Violations of Choice (SVC) holds, Ple…

Independence Axioms in Social Ranking
Takahiro Suzuki, Michele Aleandri, Stefano Moretti
https://arxiv.org/abs/2506.21836 https://arx…

Independence Axioms in Social Ranking
Independence from non-essential changes in input information is a widely recognized axiom in social choice theory. This independence reduces the cost of specifying and/or analyzing non-essential data. This study makes a comprehensive analysis of independence axioms in the context of social ranking solutions (SRSs). We consider seven independence axioms (two of which are new) and provide a novel characterization of the lexicographic excellence solution and plurality by substituting these indepen…

I've been reading the paper on small induction-recursion (which is really well-written btw!) and I think there might be a similar kind of terminological thingy about induction-recursion as with the "type-theoretic axiom of choice".
For context, "type-theoretic axiom of choice" is an old name for the distributivity of Π over Σ, which has nothing to do with choice. The reason it's named that is that, if you interpret ∀ as Π and ⊃ as Σ, the formulation of the axiom of choice in terms of relations
(∀ (x : X). ⊃ (y : Y). R(x, y)) − (⊃ (f : X − Y). ∀ (x : X). R(x, f(x)))
is just the distributivity of Π over Σ, which is trivial. The real mathematical content of the axiom of choice in type theory comes from the distributivity of Π over the propositional truncation, since the correct interpretation of ⊃ x. P x is ⊥ Σ x. P x ⊥.
Similarly, "induction-recursion" is made up of two parts: small induction-recursion, which is equivalent to indexed inductive definitions and thus rather anodyne, and the resizing of those definitions so that they live in U when they should live in U⁺, which is where the expressive power of IR comes from.
So, while "type-theoretic axiom of choice" is a very strong name for something innocuous, "induction-recursion" is an innocuous name for something very strong, essentially for dual reasons.
I hope this is not too obvious; I sure wish someone had explained this to me the first time I learned about induction-recursion.

Justified Representation: From Hare to Droop
Matthew M. Casey, Edith Elkind
https://arxiv.org/abs/2508.00811 https://arxiv.org/pdf/2508.00811

Justified Representation: From Hare to Droop
The study of proportionality in multiwinner voting with approval ballots has received much attention in recent years. Typically, proportionality is captured by variants of the Justified Representation axiom, which say that cohesive groups of at least $\ell\cdot\frac{n}{k}$ voters (where $n$ is the total number of voters and $k$ is the desired number of winners) deserve $\ell$ representatives. The quantity $\frac{n}{k}$ is known as the Hare quota in the social choice literature. Another -- more …

A probabilistic look at the infinite hat-guessing game
Nathaniel Eldredge
https://arxiv.org/abs/2508.02828 https://arxiv.org/pdf/2508.02828

A probabilistic look at the infinite hat-guessing game
In this note, we look at a hat-guessing game, in which each player must guess the color of their own hat while only seeing the hats of the other players. We focus on the case of two hat colors and a countably infinite number of players. By strategizing in advance, the players can, in some ways, do much better than random guessing; using the axiom of choice, they can in fact achieve highly counter-intuitive success. We review some of these results. Then, we use tools from probability to obtain b…

Infinite-Exponent Partition Relations on the Real Line
Lyra A. Gardiner
https://arxiv.org/abs/2507.12361 https://arxiv.org/pdf/2507.12361

Infinite-Exponent Partition Relations on the Real Line
We extend the theory of infinite-exponent partition relations to arbitrary linear order types, with a particular focus on the real number line. We give a complete classification of all consistent partition relations on the real line with countably infinite exponents, and a characterisation of the statement "no uncountable-exponent partition relations hold on the real line", working throughout in ZF without the Axiom of Choice.

Permutation Models Arising From Topological Ideals
Justin Young
https://arxiv.org/abs/2507.05371 https://arxiv.org/pdf/2507.05371

Permutation Models Arising From Topological Ideals
A recent paper by Zapletal arXiv:2404.10612 discusses permutation models of set theory which arise from dynamical ideals and highlights properties of the dynamical ideal which relate to fragments of choice in the permutation model. In this paper, we provide several examples from topology which illustrate using these connections to argue that the corresponding permutation model satisfies either the axiom of countable choice or well-ordered choice.

This https://arxiv.org/abs/2502.14879 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_eco…

Limited attention and models of choice: A behavioral equivalence
We show that many models of choice can be alternatively represented as special cases of choice with limited attention (Masatlioglu, Nakajima, and Ozbay, 2012), singling out the properties of the unobserved attention filters that explain the observed choices.For each specification, information about the DM's consideration sets and preference is inferred from violations of the contraction consistency axiom, and it is compared with the welfare indications obtained from equivalent models. Remarkabl…