Can we elect if we cannot compare?
Bibliographic record
Abstract
The aim of this paper is to study the computational power of the qualitative model, where entities are given distinct labels which are however mutually incomparable; this model is opposed to the quantitative model, where labels are integers. The qualitative model captures, for example,the case when the labels are written in different alphabets (e.g., Cyrillic, Latin) and there is no a priori agreement on a common encoding. We investigate the qualitative model through the problem of leader election in a distributed mobile environment. All known leader election protocols assume that the initial input values are distinct and pairwise comparable. While distinctness of the input values is clearly required, the comparability assumption is questionable. Our concern is whether it is possible to remove this comparability assumption. To focus solely on this concern, we consider theproblem in its weakest setting: anonymous highly symmetric networks (i.e.,Cayley graphs). In this way, to break the symmetry (and thus elect a leader) among the incomparable mobile agents, we can not rely on the existence of distinguished node labels nor on any topological asymmetry of the network. We describe a generic election protocol which is effective for all anonymous Cayley graphs; i.e., it solves the election problem if the problem is solvable, otherwise it determines that the problem is not solvable. For arbitrary networks, our protocol is conditionally effective; that is, it performs election of one agent among any set of agents in any network, under some weak conditions on the network and on the initial positions of the agents. Our work is a first step toward a better understanding of the inherent differences between "quantitative computing" where parameters are taken from a total order, and "qualitative computing" where parameters are taken from a partial order.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.027 | 0.106 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.008 | 0.025 |
| Scholarly communication | 0.015 | 0.044 |
| Open science | 0.004 | 0.009 |
| Research integrity | 0.006 | 0.009 |
| Insufficient payload (model declined to judge) | 0.034 | 0.012 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".