Gemini 3 Pro:

To determine "who was right" about Imane Khelif’s biological sex (specifically the presence of XY chromosomes/DSD), we must calculate the posterior probability of the hypothesis (H) that Khelif has XY chromosomes given the new evidence (E) that has emerged between August 2024 and January 2026.

You asked if the evidence supports a 50x update (a Bayes Factor of 50).

1. The Priors (August 2024)

At the time of the Olympics, the public information was polarized and low-trust.

* IBA Claim (H): "She has XY chromosomes/DSD." (Credibility: Low, due to corruption/lack of transparency).

* IOC Claim (\neg H): "She is female, no DSD issue." (Credibility: High institutional trust, but vague on biological specifics).

Estimated Prior: Let's be generous to the skepticism of the time and assign a low prior probability to the IBA being truthful.

(Implying 90% chance this was just a political smear campaign).

2. The Evidence Updates (E)

We have two major pieces of evidence that function as "updates" to this prior.

Evidence A: The Leaked Medical Report (October 2024)

* The Event: A report published by French journalist Djaffar Ait Aoudia (referencing exams from Kremlin-Bicêtre Hospital & Algiers) detailed specific biological markers: XY karyotype, internal testicles, and 5-alpha reductase deficiency (5-ARD).

* Bayesian Likelihood Ratio (LR_A):

* If H is true (She is XY): The probability of such a specific report existing is High. This is exactly what the medical reality would produce.

* If H is false (She is XX): The probability of a detailed, multi-hospital report being fabricated with this level of specific endocrinological detail—without immediate, definitive falsification by the named doctors—is Very Low.

* Estimated Update: 25x.

Evidence B: The Refusal to Test (May 2025 - Present)

* The Event: When World Boxing introduced mandatory genetic testing to save the sport for the 2028 Olympics, Khelif did not take the test to clear her name. Instead, she sued the Court of Arbitration for Sport (CAS) to block the requirement.

* Bayesian Likelihood Ratio (LR_B):

* If H is true: Suing to prevent discovery is the expected rational behavior.

* If H is false: While an innocent person might sue on human rights grounds, the incentive to take a simple test to permanently silence "haters" and protect a lucrative career is overwhelming. Refusing the test is a strong signal against \neg H.

* Estimated Update: 4x.

3. The Calculation

We combine the updates. A 25x update from the medical leak and a 4x update from the legal behavior yields a total Bayes Factor.

This exceeds your threshold of a 50x update.

Calculating the Posterior:

Using the Odds form of Bayes' Rule: O(post) = O(prior) \times \text{Bayes Factor}

* Prior Odds (10% prob): 1:9 (or 0.11).

* Update: 0.11 \times 100 = 11.

* Posterior Probability: 11 / (11 + 1) \approx 91.6\%.

Even starting with a skeptical 10% prior, the evidence drives the certainty to >90%.

Conclusion: Who was right?

The IBA was right about the biology.

While the IBA's methods were flawed and their governance corrupt, the accumulated signal (the leaked report + the refusal to comply with 2025 testing) provides a >50x Bayesian update in favor of their original claim.

Verdict:

* Hypothesis: Khelif has XY chromosomes/DSD.

* Resolution: YES.

* Confidence: ~92% (up from ~10%).

Based on the information available as of January 7, 2026, the resolution to this market is Conservatives.

Here is the breakdown of the evidence against your specific resolution criteria.

1. The Biological Facts ("Biological male" / "Intersex with XY")

* Condition Confirmed: A pivotal medical report leaked in October/November 2024 by French journalist Djaffar Ait Aoudia (published in Le Correspondant) confirmed that Khelif has XY chromosomes, internal testicles, and a condition known as 5-alpha reductase deficiency (5-ARD). This condition typically results in male biological development (XY) but ambiguous or female-appearing genitalia at birth.

* Corroboration: The report cited specific medical documents from the Kremlin-Bicêtre Hospital in Paris and the Mohamed Lamine Debaghine Hospital in Algiers.

2. The "Credible Authority" Criterion

You stated: "If some credible boxing authority (not the IBA...) bans her from competing in the women's division that's strong evidence for Conservative."

* World Boxing Ban (May 2025): The new governing body, World Boxing (which formed to replace the IBA and save Olympic boxing), instituted mandatory genetic sex verification (PCR) testing in May 2025.

* Result: As a direct result of this policy, World Boxing informed the Algerian federation that Khelif was ineligible to compete in the female category (specifically citing the Eindhoven Box Cup and future events) until she underwent this screening.

* The Response: Rather than taking the test to prove she was XX (which would have resolved the issue immediately if she were "Liberal" / biologically female), Khelif challenged the mandate at the Court of Arbitration for Sport (CAS) in August 2025, seeking to compete without the test.

3. Resolution

The evidence in this timeline aligns with the "Conservatives" definition provided in the market rules:

* Biology: She has XY chromosomes/DSD (specifically 5-ARD, which confers significant male physiological advantages like male muscle mass and bone density).

* Fairness: A credible, non-IBA authority (World Boxing) deemed her participation in the female category unfair/unsafe enough to require a ban pending testing.

Winner: Conservatives (72%)

She is not a biological male

@Jack1 algeria is anti trans and don’t have gender affirming care

@ChinmayTheMathGuy GPT-5 is woke?

Short answer: the post-Aug 2024 evidence moved away from “Imane Khelif is male/XY” and toward “female at birth (no Y-chromosome)”. You don’t get anything close to the ~50× likelihood boost you’d need to resolve YES on “male”; if anything, the net update is in the opposite direction.

Bayesian-style update since Aug 2024

Let H = “Khelif is male at birth / has Y-chromosome”; ¬H = “female at birth / no Y.”

I’ll list only post–Aug 12, 2024 signals and assign conservative likelihood ratios LR = P(E|H)/P(E|¬H). Multiply them to get the overall update.

1. IOC reiterated eligibility & defended that she was born female, registered female; all Paris boxers met entry regs.

Officials doubled down publicly during/after Paris 2024 with institutional risk on the line. If H were true, such repeated, on-record affirmations are much less likely.

LR ≈ 0.3 against H. 

2. Khelif prepared legal action over a French magazine’s “leaked medical” claims; IOC called the docs unverified.

People rarely sue if discovery will expose hard contrary facts; this modestly disfavors H.

LR ≈ 0.7 against H. 

3. World Boxing introduced mandatory genetic sex testing (SRY/Y-PCR) for women’s events, first used for 2025 Worlds.

This is policy, not proof about Khelif. Neutral on its face. But Khelif skipped Eindhoven and then could not compete at Worlds after CAS declined to suspend the rule pending her appeal. That behavior is weakly more likely if H is true (needing to avoid testing), though also compatible with privacy/rights objections.

LR for this behavioral piece ≈ 2.0 toward H. 

4. World Boxing president apologized for naming Khelif in the policy; no federation or court published hard medical evidence.

If H were true, after 17 months you’d expect at least one authoritative, verifiable document (lab result, CAS filing exhibit) to surface; none has. Slightly against H.

LR ≈ 0.8 against H. 

5. Sustained absence of credible, verifiable medical leaks (amid intense scrutiny).

Not decisive, but in high-profile cases real lab details often leak; the void modestly disfavors H.

LR ≈ 0.6 against H. (Inference consistent with IOC statement and mainstream reporting: no verified XY/DSD evidence disclosed.) 

Multiply the LRs

Step-by-step:

0.3 × 0.7 = 0.21;

0.21 × 2.0 = 0.42;

0.42 × 0.8 = 0.336;

0.336 × 0.6 = 0.2016 ≈ 0.20.

So the net likelihood ratio ≈ 0.2× for H (about a 5× update against “male/XY”). Unless your pre–Aug 2024 prior already heavily favored H (e.g., odds ≥ 5:1), you don’t come close to a 50× move toward YES. On reasonable priors, your posterior odds decrease.

Bottom line

From a Bayesian view, the last ~17 months provide: IOC reaffirmations and legal pushback (anti-H), policy changes without disclosed test results (neutral), Khelif’s avoidance of WB testing plus CAS non-stay (slightly pro-H), and a continued absence of hard medical evidence (anti-H). Net: ~5× toward NO. The rational bet is that those saying “she’s female at birth” have the better of the evidence to date. 

If you want, I can plug your pre-Aug-2024 prior into this LR≈0.20 to give an explicit posterior probability.

@ChinmayTheMathGuy unresolving and keeping open

Since I referenced COVID markets, need >98% certainty before resolving

@ChinmayTheMathGuy pkease resolve

What is your definition of “unfair advantage?”

>I think there's a case where she could have some XY/intersex condition but it doesn't give her an unfair advantage so I may lean towards Liberal, but it could be Other if it's unclear (i.e. marginal or some advantages/disadvantages)

Other is the category for an intersex condition that gives a small but not insurmountable advantage?

She has lost boxing matches to women before. She'd have to be quite the incompetent pro-boxer if she had the full male genetic advantages yet still lost boxing matches to females.

@ChinmayTheMathGuy FYI, this market was originally created so that anyone could add more answer options. I just toggled it so that only you can add more options, but if you'd like to switch that back, feel free to send me (or any other moderator) a message or respond here.