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Improved Approximation Guarantees for Groupwise Maximin Share Fairness
Georgios Amanatidis, Anna Korfiati, Evangelos Markakis, Christodoulos Santorinaios
https://arxiv.org/abs/2606.04731 https://arxiv.org/pdf/2606.04731 https://arxiv.org/html/2606.04731
arXiv:2606.04731v1 Announce Type: new
Abstract: We study the problem of fairly allocating a set of indivisible goods to a set of $n$ agents with additive valuation functions. We focus on the very demanding notion of \textit{groupwise maximin share fairness} (GMMS), which requires that each agent $i$ receives value comparable to their maximin share, where the latter is computed \textit{with respect to any subset of agents that contains $i$}. We show that it is possible to compute $(\phi-1)$-approximate GMMS allocations in polynomial time, where $\phi \approx 1.618$ is the golden ratio). This improves on the previously known guarantee of $4/7$ of Chaudhury et al. [SICOMP; 2021] and Amanatidis et al. [TCS; 2020]. We propose a simple algorithm that maintains the same main properties as the Draft-and-Eliminate algorithm of Amanatidis et al. [TCS, 2020] and we improve on the approximation guarantee analysis by carefully bounding the relevant value within any subinstance induced by the restriction of our allocation to a subset of agents. Our analysis is asymptotically tight for algorithms that share these properties and has the additional benefit of giving improved guarantees for restricted settings; in particular, when the agents agree on the top $n$ goods or when the number of agents is small. To illustrate the challenges of going beyond the guarantees of our algorithm, we also present a variant with an improved approximation of $(\sqrt{10}-1)/3 \approx 0.72$ for the case of three agents. To achieve this improvement we partially characterize the maximin share guarantees of short picking sequences for a small number of goods.
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Three paragraphs, from three different hotel reviews.
Can you tell which, if any, were AI‑generated?
🔸“The hotel is in a great location for everything. Lots of places to eat and drink. The hotel itself is always abuzz. The tavern located on the ground floor is definitely a must. Food, service, prices and atmosphere were great.”
🔸“A good hotel, though the room had the proportions of a well-appointed lift. Slept well, shower was excellent, staff were friendly. Breakfast was bus…

We're up to the stage in the Kinship Carers assessments where we have to ask 4 of our friends to give us references (2 each) when CYF calls them. That's my task for this afternoon.
It's a difficult choice because:
1. No one I know likes to answer unknown numbers.
2. My closest friends are also friends with husband but he has no others.
3. I hate asking.
#Grandparenting

Nothing really new or groundbreaking from the how to reclaim your attention economy, just a quick and useful refresher by Daniel Pink.
Via #PsycheMag
https://youtu.be/ZXHrPfWJcCI?is=RYlCJz

I've been doing some family history via ancestry.com and they regularly notify my about new documents that may relate to our family tree. Today I got a report from the 1930 police gazette about a cow that was stolen from my grandfather. I love the language in these reports, they are a slice of history.

Welfare Maximization in Bilateral Trade: Improved Approximation Guarantees Beyond the Fixed Price Barrier
Shahar Dobzinski, Ariel Shaulker
https://arxiv.org/abs/2606.04890 https://arxiv.org/pdf/2606.04890 https://arxiv.org/html/2606.04890
arXiv:2606.04890v1 Announce Type: new
Abstract: We study the setting of welfare maximization in bilateral trade, where the values of both the buyer and the seller are drawn from independent distributions. Our goal is to maximize social welfare. In this setting, fixed price mechanisms have been extensively studied. In a fixed price mechanism, there is a price $p$ that depends only on the distributions of the buyer and the seller. Trade occurs if and only if the buyer's value is at least $p$ and the seller's value is at most $p$. A long line of work has culminated in determining almost exactly the approximation ratios achievable by fixed price mechanisms: there exists a fixed price mechanism that obtains at least a $0.72$ fraction of the social welfare, but no fixed price mechanism can guarantee more than a $0.7381$ fraction of it [Cai and Wu, STOC'23; Liu, Ren, and Wang, STOC'23]. No other incentive-compatible mechanism is known to beat the performance of fixed-price mechanisms in this setting.
This paper shows how to achieve a larger fraction of the optimal welfare with other classes of mechanisms. Specifically, we study the buyer-offering mechanism with a reserve price. In this mechanism, the buyer observes its value and makes a take-it-or-leave-it offer to the seller, where the offer is at least the reserve price. Beyond its simplicity, this natural mechanism is attractive because the seller always has a dominant strategy: accept the offer if its value is at most the offer, and otherwise reject it. We show that there always exists a reserve price that guarantees a $0.746$ fraction of the social welfare. This not only improves upon the best previously known approximation guarantee for the problem, but also demonstrates that fixed-price mechanisms are not optimal in this setting.
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RE: https://c.im/@cdarwin/116858479856697478
The masqueraders and pretenders parade around in grand performative acts of love of God and country ...
while willfully betraying both
—the rest of us are going to have to fight to hold on to our nation
and…

Non-obvious Manipulability in the Additively Separable Group Activity Selection Problem
Maria Fomenko (Gran Sasso Science Institute), Giovanna Varricchio (University of Calabria)
https://arxiv.org/abs/2606.05048 https://arxiv.org/pdf/2606.05048 https://arxiv.org/html/2606.05048
arXiv:2606.05048v1 Announce Type: new
Abstract: In this work, we study the additively separable Group Activity Selection Problem (AS-GASP) in an imperfect information setting, where agents have private preferences over activities and weights over other agents. Our goal is to design mechanisms that assign agents to activities based on their declared preferences and weights, with the objective of maximizing social welfare while ensuring truthful reporting. We, therefore, focus on the notion of non-obvious manipulability (NOM), a form of resilience to manipulation. We first investigate the relationship between NOM and social welfare optimality. In this regard, our main result shows that, when preferences and weights are arbitrary or non-negative, any optimal mechanism is non-obviously manipulable. In contrast, when either preferences or weights are binary, we show that optimality and NOM may be incompatible. We then turn to computational aspects. While it is known that computing an optimal outcome for the AS-GASP is NP-hard even in restricted settings, we establish a strong inapproximability result showing that no polynomial-time algorithm can guarantee a bounded approximation ratio when preferences and weights may take arbitrary values. In turn, when preferences are non-negative, we show that a bounded approximation is possible, and we present two asymptotically optimal approximation mechanisms that are also guaranteed to satisfy NOM.
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