Election predictions are arbitrage-free: response to Taleb
Pith reviewed 2026-05-25 10:32 UTC · model grok-4.3
The pith
Probabilistic election forecasts are arbitrage-free under mild assumptions
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Under mild assumptions, probabilistic forecasts for political elections cannot be arbitraged: no portfolio of bets on the outcomes can be constructed with non-positive cost, non-negative payoff in every scenario, and positive payoff in at least one scenario. The heuristic used to detect apparent violations in the 2016 forecasts is therefore false.
What carries the argument
No-arbitrage condition applied directly to election-outcome probability forecasts treated as asset prices.
If this is right
- Forecasts of the 2016 U.S. election did not violate arbitrage boundaries.
- No adjustment to published election probabilities is required to restore no-arbitrage.
- No-arbitrage pricing supplies no diagnostic for detecting errors in these forecasts.
- The same conclusion applies to any political election whose outcomes meet the mild assumptions.
Where Pith is reading between the lines
- If the assumptions hold for real betting markets, then forecasts from different sources can be used together without creating arbitrage.
- The result may extend to non-election prediction markets that share similar outcome structures.
- Critiques that rely on arbitrage tests must first verify whether the mild assumptions are met in the specific setting.
Load-bearing premise
The mild assumptions about market completeness and outcome structure that are required to prove every forecast is arbitrage-free.
What would settle it
Exhibit a concrete set of election probabilities, together with a portfolio of bets, that produces a guaranteed non-negative payoff with positive probability in some outcome while having non-positive net cost, all while satisfying the paper's mild assumptions.
read the original abstract
Taleb (2018) claimed a novel approach to evaluating the quality of probabilistic election forecasts via no-arbitrage pricing techniques and argued that popular forecasts of the 2016 U.S. Presidential election had violated arbitrage boundaries. We show that under mild assumptions all such political forecasts are arbitrage-free and that the heuristic that Taleb's argument was based on is false.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper responds to Taleb (2018) by claiming that, under mild assumptions, every probability measure on a finite set of election outcomes is arbitrage-free in the associated market, rendering Taleb's heuristic for detecting arbitrage violations in 2016 U.S. Presidential forecasts false. The argument is presented as a general no-arbitrage result that applies to any such political forecast.
Significance. If the central claim holds, the result would show that Taleb's no-arbitrage critique of election forecasts rests on an invalid heuristic and that standard probabilistic forecasts cannot violate arbitrage bounds under the stated conditions. This would limit the applicability of arbitrage-based diagnostics to election prediction markets. The manuscript does not supply machine-checked proofs or reproducible code.
major comments (2)
- [Abstract and §2] The central claim rests on 'mild assumptions' whose precise statement and verification against real election markets are not load-bearing in the provided text. If these assumptions require a complete market in which every contingent claim on the finite outcome space can be replicated without friction, the result does not rule out static arbitrage among the actually traded contracts (national winner, selected state contracts) that were the basis of Taleb's original examples.
- [§3] The demonstration that the heuristic is false appears to rely on constructing an equivalent martingale measure for any probability assignment. This construction is not shown to remain valid when the market is incomplete and only a proper subset of Arrow-Debreu securities is traded, which is the relevant setting for 2016 election contracts.
minor comments (1)
- [§2] Notation for the outcome space and the set of traded contracts should be introduced with explicit definitions before the no-arbitrage argument begins.
Simulated Author's Rebuttal
We thank the referee for the careful reading and constructive comments. Below we respond point-by-point to the major comments. We will revise the manuscript to make the assumptions explicit and to clarify applicability to incomplete markets.
read point-by-point responses
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Referee: [Abstract and §2] The central claim rests on 'mild assumptions' whose precise statement and verification against real election markets are not load-bearing in the provided text. If these assumptions require a complete market in which every contingent claim on the finite outcome space can be replicated without friction, the result does not rule out static arbitrage among the actually traded contracts (national winner, selected state contracts) that were the basis of Taleb's original examples.
Authors: The mild assumptions are finiteness of the outcome space together with the absence of transaction costs and other frictions; they do not include or require market completeness. Under these conditions any probability measure on the finite outcomes defines prices for the traded contracts (national winner, state contracts) via expectation, and the first fundamental theorem of asset pricing guarantees the absence of arbitrage. This holds for any subset of contracts. We will revise §2 to state the assumptions explicitly and add a short verification of their relevance to the 2016 market structure. revision: yes
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Referee: [§3] The demonstration that the heuristic is false appears to rely on constructing an equivalent martingale measure for any probability assignment. This construction is not shown to remain valid when the market is incomplete and only a proper subset of Arrow-Debreu securities is traded, which is the relevant setting for 2016 election contracts.
Authors: The construction remains valid in incomplete markets. Given any probability measure P, the prices of the actually traded contracts are set to their expectations under P; P is then an equivalent martingale measure for that (incomplete) market, so the fundamental theorem precludes arbitrage. Completeness is not used. We will add a clarifying sentence in the revision of §3 emphasizing that the argument applies directly to the incomplete market of 2016 contracts. revision: yes
Circularity Check
No circularity; mathematical demonstration is self-contained against external benchmark.
full rationale
The paper advances an independent no-arbitrage argument under explicitly stated mild assumptions on the market structure and probability measures. The central claim is derived from first-principles replication arguments rather than any fitted parameter, self-definition, or load-bearing self-citation. Taleb (2018) is treated as an external reference whose heuristic is directly falsified by the new construction; no step reduces the result to the paper's own inputs by construction. The derivation therefore remains non-circular even if the applicability of the assumptions to real election markets is debatable on other grounds.
discussion (0)
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