A categorical market lists several mutually exclusive outcomes—nominees in a primary, teams in a group stage, Oscar contenders—and asks which single label wins. Each outcome is often implemented as its own YES/NO slice, but economically you are trading a partition of probability: the prices should live on a simplex and sum to roughly 100%.
One winner, many tickets
In a winner-take-all race, exactly one outcome resolves YES; every other pays $0. If Candidate A trades at 42¢, B at 35¢, and C at 28¢, the raw mids sum to 105¢—a 5¢ overround. Buying one share of each outcome costs $1.05 for a guaranteed $1 payout at settlement, a structural loss unless fees are rebated or you are deliberately harvesting a mispricing.
When the sum of asks is below 100¢, buying the full slate can resemble a Dutch-book trade: pay 97¢, receive $1, keep 3¢ before fees. Real markets compress these gaps when arbitrageurs are active; on capped retail venues, wide spreads can leave sums distorted longer than on deep regulated books.
Normalizing when the simplex is messy
Traders often convert raw mids to a normalized vector that sums to 1. With mids 0.42, 0.35, 0.28 totaling 1.05, normalized beliefs are roughly 40%, 33%, and 27%. Compare your distribution to that normalized vector, not to raw mids alone, when arguing the market is wrong on B.
Your own probabilities should sum to 1 across the exclusive slate. If you assign 38% to A, 33% to B, and 29% to C, the largest edge might be on B even if C looks “cheapest” in cents—cheap price is not the same as positive expected value.
Worked edges in prose
Suppose your model gives A 38% while the market mid is 42%—fade A if the ask confirms. B at 35% versus your 33% might be a small negative unless the ask is lower than your executable threshold. C at 28% versus your 29% could be a modest buy if the ask is 26¢ and fees are small. Portfolio expected value requires a coherent vector, not three unrelated hunches.
After a front-runner drops out, reprice the survivors on the new simplex. Old C prices are stale the moment the withdrawal is official.
When the menu changes
Candidates withdraw, games cancel, or rules add an Other bucket. After A drops out, the remaining outcomes must be repriced on the surviving simplex. Conditional probability matters: the chance B wins given A is out is not the opening price printed when A was still in the race.
Primary slates and general-election slates are different partitions—“wins nomination” is not “wins the presidency.” Cross-contract relationships apply only when resolution text and timing align.
Longshots and base rates
A 4¢ longshot implies the market sees about a 4% chance. If your model says 1%, the YES buy is negative expected value despite the low price—favorite-longshot bias and overround on tails punish lottery tickets. Favorites near 90¢ carry lower per-share variance but still tail risk on the NO side.
Log scoring from the probability module punishes confident wrong tails; calibration on longshots is where forecasters often look sharp on paper and bleed in practice.
Liquidity across the slate
Favorites tend to have tighter books; tails are wide on order-book venues and slippery on AMM curves. Expressing a view on the second choice may mean trading a liquid leg and hedging elsewhere, not forcing size into a 6¢ ask with no depth.
Multi-outcome pages on crypto venues sometimes pool liquidity differently from separate tickers on regulated exchanges—scan all legs before declaring the simplex sum.
Nested binaries that look categorical
“Who wins the nomination?” may appear as one page with many tokens or as separate binaries per name. Either way, exclusivity is a rule claim, not a UI convenience. Committee chairs, third-place finishes, and “top two” slates are not interchangeable menus.
A brief comparison: poll slice vs market slate
| Lens | What it captures | Weak spot |
|---|---|---|
| Poll of “who would you vote for” | Stated preference at a snapshot | Slow to update; sampling bias |
| Categorical market | Prices traders accept today | Thin tails; rule differences |
Markets do not replace polls; they price risk capital under specific contract rules.
Dutch-book intuition without a spreadsheet
If asks on three exclusive outcomes sum to 97¢, you pay 97¢ for $1 guaranteed at settlement—a 3¢ gross edge before fees. If the sum is 105¢, you pay $1.05 for $1—a loss unless you are fading specific legs with independent edge. Overround is not moral failure; it is liquidity and vig. Compression toward 100% is the arb dial.
PredictIt-style frictions
Low per-market share caps and wide spreads can leave sums away from 100% longer than on deep regulated books. Academic-style profit fees shrink Dutch-book edge. Use such venues for belief discovery; size elsewhere when caps allow.
Bayes when the slate shrinks
When a candidate exits, update beliefs on survivors so the vector sums to one. The price of B after A drops is P(B | not A), not the stale opening print. Debate nights and scandals move the whole simplex, not one name in isolation.
Expressing a view on a crowded race
You may fade the front-runner and add second-tier names if your vector beats normalized mids on executable asks. Hedging a primary longshot with a general-election contract is a tree problem—previewed in combination markets—not a second independent bet.
Core concepts to remember
Exclusive outcomes form a simplex near 100%. Normalize when sums drift. Renormalize after dropouts. Longshots need base rates, not cheap cents alone. Primary and general menus are different partitions.
Multi-outcome pages versus separate tickers
Whether the UI shows one page with many tokens or separate binaries per name, exclusivity is a rule claim. Scan every leg before you declare arb on the sum. Missing a tail outcome invalidates Dutch-book math.
Common mistakes
Buying three longshots thinking you diversified. Using primary prices after a dropout without renormalizing. Treating sum-of-asks at 99¢ as arb without fee schedules on profit. Folding primary and general into one mental simplex.
What comes next
Categoricals assign probability to names. The next chapter assigns it to numbers—inflation bands, vote shares, and other scalar outcomes.
Next: Scalar Markets (Range-Based Outcomes)