[polymarket][struct-arb] Type B MEE multi-outcome basket

[polymarket][struct-arb] Type B MEE multi-outcome basket — INCONCLUSIVE

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polymarketstruct-arbmee-basketinconclusive Priority: 3 Source: polymarket-struct-arb Created: 2026-05-20 Updated: 2026-05-20

Hypothesis

For mutually exclusive and exhaustive (MEE) event groups on Polymarket, $\sum_i a_i < 1$ (buy-all arb) or $\sum_i b_i > 1$ (sell-all arb) should occur when the individual YES tokens are mispriced relative to each other.

Data used

2 000 events fetched from gamma-api, 2026-05-20
MEE candidates identified by keyword heuristics (contains "range", "between", "rank", price bracket labels)
36 event groups scanned; CLOB top-of-book fetched for all YES tokens in each group

Sample — genuine MEE event:

"Where will 2026 rank among the hottest years on record?" (n=6 outcomes)
  Outcomes: hottest | 2nd-hottest | 3rd | 4th | 5th | other
  Asks:      0.330  |   0.580     | 0.023| ... | 0.005|...
  sum(asks) = 0.991  →  buy_gross = 0.009
  min(ask_depth) = 59 units  →  max_profit = 0.009 × 59 = $0.53

Method

$$\text{buy_gross} = 1 - \sum_i a_i \quad (\text{arb if} > 0)$$ $$\text{sell_gross} = \sum_i b_i - 1 \quad (\text{arb if} > 0)$$

Execution: buy one unit of every YES token; exactly one pays $\$1$ at resolution.
Size = $\min_i(\text{ask_depth}_i)$ — limited by the thinnest outcome.

Critical exclusions applied (false positives in raw scan): - Cumulative threshold events ("Gold above $6000", "above $6500"...) — NOT MEE; multiple can resolve YES simultaneously - Multiple-winner events ("Who will announce Presidential run", "Fields Medal" with up to 4 winners) — NOT MEE - Competitive primary markets ("Who will advance from primary") — top-2 advance, not MEE

Result

Event (genuine MEE)	Type	gross	max_profit	Status
Where will 2026 rank hottest?	buy-all	+0.0090	$0.53	micro-profit
What will Gold settle at Jun?	buy-all	+0.0160	$0.26	micro-profit
What will Crude Oil settle Jun?	buy-all	+0.0070	$0.01	trivial
What will Fed rate be end 2026?	sell-all	+0.0100	$0.05	trivial

False positives from non-MEE events: 7 (excluded — not arbs).

Verdict: Violations technically exist (gross > 0, fees ≈ 0 on CLOB), but are economically unactionable — max profit across all events combined is < $1 due to thin book depth on rarer outcomes. The market is well-calibrated at the MEE aggregate level; the residual gap ($\leq 1.6\,c$) is smaller than any reasonable gas or slippage estimate on a live platform.

Reproduction

source ~/.pmvenv/bin/activate
python3 /mnt/projects/tnt_85c10df4451042ca/prj_c7cb91b70b2f42ac/pm_struct_arb_scanner.py
# results: /tmp/pm_data/type_b_results.json

Failure mode / next step

New MEE events added near resolution may show larger gaps if book is thin and prices haven't been updated
A real-time alert system watching sum(asks) across all MEE groups could catch larger violations when they emerge (e.g., just after a resolution event that prices one outcome at 0 but others haven't adjusted yet)
Better MEE detection: group by eventId + require outcomes to be exhaustive partitions (check outcomePrices sum ≈ 1.0 as MEE signal instead of keyword heuristics)

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Title * Body (Markdown)

## Hypothesis
For mutually exclusive and exhaustive (MEE) event groups on Polymarket, $\sum_i a_i < 1$ (buy-all arb) or $\sum_i b_i > 1$ (sell-all arb) should occur when the individual YES tokens are mispriced relative to each other.

## Data used
- 2 000 events fetched from gamma-api, 2026-05-20
- MEE candidates identified by keyword heuristics (contains "range", "between", "rank", price bracket labels)
- 36 event groups scanned; CLOB top-of-book fetched for all YES tokens in each group

Sample — genuine MEE event:
```
"Where will 2026 rank among the hottest years on record?" (n=6 outcomes)
  Outcomes: hottest | 2nd-hottest | 3rd | 4th | 5th | other
  Asks:      0.330  |   0.580     | 0.023| ... | 0.005|...
  sum(asks) = 0.991  →  buy_gross = 0.009
  min(ask_depth) = 59 units  →  max_profit = 0.009 × 59 = $0.53
```

## Method
$$\text{buy\_gross} = 1 - \sum_i a_i \quad (\text{arb if} > 0)$$
$$\text{sell\_gross} = \sum_i b_i - 1 \quad (\text{arb if} > 0)$$

Execution: buy one unit of every YES token; exactly one pays $\$1$ at resolution.  
Size = $\min_i(\text{ask\_depth}_i)$ — limited by the thinnest outcome.

Critical exclusions applied (false positives in raw scan):
- **Cumulative threshold** events ("Gold above $6000", "above $6500"...) — NOT MEE; multiple can resolve YES simultaneously
- **Multiple-winner** events ("Who will announce Presidential run", "Fields Medal" with up to 4 winners) — NOT MEE
- **Competitive primary** markets ("Who will advance from primary") — top-2 advance, not MEE

## Result

| Event (genuine MEE) | Type | gross | max_profit | Status |
|---|---|---|---|---|
| Where will 2026 rank hottest? | buy-all | +0.0090 | **$0.53** | micro-profit |
| What will Gold settle at Jun? | buy-all | +0.0160 | **$0.26** | micro-profit |
| What will Crude Oil settle Jun? | buy-all | +0.0070 | **$0.01** | trivial |
| What will Fed rate be end 2026? | sell-all | +0.0100 | **$0.05** | trivial |

False positives from non-MEE events: 7 (excluded — not arbs).

**Verdict**: Violations technically exist (gross > 0, fees ≈ 0 on CLOB), but are **economically unactionable** — max profit across all events combined is < $1 due to thin book depth on rarer outcomes. The market is well-calibrated at the MEE aggregate level; the residual gap ($\leq 1.6\,c$) is smaller than any reasonable gas or slippage estimate on a live platform.

## Reproduction
```bash
source ~/.pmvenv/bin/activate
python3 /mnt/projects/tnt_85c10df4451042ca/prj_c7cb91b70b2f42ac/pm_struct_arb_scanner.py
# results: /tmp/pm_data/type_b_results.json
```

## Failure mode / next step
- New MEE events added near resolution may show larger gaps if book is thin and prices haven't been updated
- A real-time alert system watching `sum(asks)` across all MEE groups could catch larger violations when they emerge (e.g., just after a resolution event that prices one outcome at 0 but others haven't adjusted yet)
- Better MEE detection: group by `eventId` + require outcomes to be exhaustive partitions (check `outcomePrices` sum ≈ 1.0 as MEE signal instead of keyword heuristics)

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