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% Section 2: Institutional Setting and Related Literature
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\section{Institutional Setting and Related Literature}\label{sec:literature}

\subsection{Polymarket and negative-risk markets}\label{subsec:institutions}

Polymarket is a prediction-market platform on the Polygon blockchain. Each binary market issues a pair of outcome tokens, YES and NO, through a conditional-token contract: one unit of the USDC stablecoin can be split at any time into one YES and one NO token, and a YES--NO pair can be merged back into one USDC. At resolution the winning token redeems for one USDC and the losing token for nothing. Orders are matched off-chain on a central limit order book operated by the platform and settled on-chain; the order book, trade history and settlement are public. Resolution is delegated to the UMA optimistic oracle: anyone may propose an outcome by posting a bond, the proposal can be disputed during a challenge window, and disputed resolutions are decided by a vote of UMA token holders.\footnote{Polymarket documentation, \url{https://docs.polymarket.com} (consulted 17 October 2026). The documentation describes a proposal bond of about \$750, a two-hour challenge window, and a dispute process of four to six days.}

Multi-outcome questions are organised as \emph{negative-risk} events. The outcomes of such an event are mutually exclusive by construction, and the platform's adapter contract allows a NO token on any one outcome to be converted at any time into one YES token on each of the other outcomes. The conversion embodies the accounting identity that betting against one outcome is equivalent to betting on all the others. For an event with $N$ outcomes, it implies that a trader holding one NO token on every outcome holds a claim worth $N-1$ dollars at resolution---exactly one of the $N$ NO tokens expires worthless---and the adapter lets this position be unwound before resolution. The event studied in this paper, ``Fed decision in June?'', lists five outcomes defined on the change in the upper bound of the target federal funds range decided at the June 2026 FOMC meeting: a decrease of 50 basis points or more, a decrease of 25 basis points, no change, an increase of 25 basis points, and an increase of 50 basis points or more. These five outcomes are exhaustive, so the five YES tokens form a complete set of state claims on the decision. The same structure applies to the ``Presidential Election Winner 2024'' event with seventeen candidate contracts, where the last contract (``Other'') completes the state space.

Two features of the setting matter for the interpretation of prices. First, prices are quoted in USDC and USDC held as collateral earns no interest on the platform, so that the time value of money is not neutralised by the settlement design as it is in a margined futures contract. Second, the fee structure differs across markets: the metadata of the five Fed contracts report no trading fee at the time of the snapshot, whereas the platform introduced taker fees on short-dated cryptocurrency markets in early 2026 and announced an extension to other categories. We treat the fee on the markets studied as zero and discuss this assumption in Section~\ref{sec:results}.

\subsection{Prices, probabilities and risk}

The interpretation of prediction-market prices as probabilities is the central theme of the literature surveyed by \citet{wolfers2004prediction}, \citet{wolfers2006theory} and \citet{snowberg2013prediction}. \citet{manski2006interpreting} showed that, with risk-neutral traders who hold heterogeneous beliefs and face budget constraints, the equilibrium price of a binary contract need not equal the mean belief and can lie anywhere in an interval determined by the distribution of beliefs. \citet{wolfers2006interpreting} replied that with logarithmic utility the price equals the wealth-weighted mean belief, and that for plausible preference parameters the gap between price and mean belief is small except near the extremes. \citet{ottaviani2015price} derived the dynamics of such prices under heterogeneous beliefs and wealth effects and showed that they underreact to news, producing momentum and reversal. The empirical calibration literature finds that prices are informative but not perfectly calibrated: long-run evidence from the Iowa Electronic Markets \citep{berg2008results}, the favourite--longshot pattern documented by \citet{page2013calibrated}, and the comparison of markets and polls in \citet{rothschild2009forecasting} all point to systematic but modest deviations. \citet{rhode2004historical} show that the large historical betting markets on U.S.\ presidential elections behaved in much the same way a century ago.

The present paper takes a different route to the same question. For an event whose states are correlated with aggregate wealth---a monetary-policy decision is the leading example---the price of each state claim is $\psi_j = \delta\,q_j$ where $\delta$ is a discount factor and $q_j$ a risk-neutral probability. Dividing by the sum of state prices recovers $q_j$ exactly, whatever the risk attitudes of traders, but the physical probability remains unidentified without further assumptions. \citet{piazzesi2008futures} document economically large and time-varying risk premia in federal funds futures, the natural benchmark for our Fed contracts; we therefore interpret our normalised prices as risk-neutral quantities throughout and treat the recovery of physical probabilities as outside the scope of the data.

\subsection{Monetary-policy expectations and macroeconomic news}

A large literature uses market prices to measure monetary-policy expectations and their revisions around announcements. \citet{kuttner2001monetary} extracts policy surprises from federal funds futures; \citet{gurkaynak2005actions} show that FOMC statements move expectations through a second ``path'' factor beyond the current-rate surprise; \citet{bernanke2005explains} and \citet{rigobon2004impact} estimate the response of equity prices to those surprises; \citet{nakamura2018high} document that announcements also convey information about the economy. The announcement-day variance approach, in which the arrival of scheduled information is identified by comparing the variance of price changes on release days with that on other days, goes back to \citet{ederington1993markets} for interest-rate futures and to \citet{andersen2003micro} for high-frequency exchange rates, and the distinction between calendar time and trading time in the arrival of information to \citet{french1986stock}. Our announcement-day analysis of the Polymarket-implied expected policy change follows this tradition with daily data, exploiting the fact that the platform trades on weekends.

\subsection{Price discovery across venues}

When the same asset trades in several markets, the contribution of each venue to the common efficient price can be measured by the information share of \citet{hasbrouck1995one} or the common-factor weights of \citet{gonzalo1995estimation}; \citet{baillie2002price} and \citet{yan2010structural} discuss the relation between the two and the conditions under which either is informative. Both measures require the prices to be cointegrated with a known cointegrating vector, which is the case for the same security on two exchanges or for a futures contract and its underlying index \citep{hasbrouck2003intraday}. It is not the case for a binary contract on an FOMC decision and the ten-year Treasury yield or an equity index: the contract price is bounded in $[0,1]$, converges to zero or one, and is related to conventional asset prices through a non-linear and time-varying mapping. We therefore do not compute information shares and rely instead on Granger-causality tests in first differences \citep{granger1969investigating,sims1980macroeconomics,lutkepohl2005new}, with the limitations discussed in Section~\ref{sec:methodology}. The cross-venue comparison of modern prediction markets themselves has recently been taken up by \citet{ng2025price}, who compare Polymarket, Kalshi and PredictIt around the 2024 election and find that the more liquid venue leads, and by \citet{chernov2025comovement}, who combine state-level election contracts with polls to estimate the comovement of voter preferences. \citet{reichenbach2025exploring} study calibration and trader skill on Polymarket. None of these papers examines the pricing of complete state spaces or the Fed decision markets.

\subsection{Microstructure of blockchain markets}

The microstructure concepts we use are standard: the adverse-selection view of spreads \citep{glosten1985bid,kyle1985continuous}, the serial-covariance spread estimator of \citet{roll1984simple}, and the surveys of \citet{ohara1995market} and \citet{madhavan2000market}. Two strands of the cryptocurrency literature are directly relevant. \citet{makarov2020trading} document large and persistent arbitrage deviations across cryptocurrency exchanges, attributable to capital controls and settlement frictions; the complete-set arbitrage on a negative-risk event is simpler, because all legs settle on one platform in one collateral, and it is therefore a cleaner test of whether blockchain markets enforce the law of one price. \citet{cong2023wash} show that reported volumes on unregulated cryptocurrency exchanges are heavily inflated by wash trading; we do not use volume as an input to any test, but the point cautions against reading Polymarket's reported volumes as measures of genuine participation. \citet{harvey2021defi} provide an overview of the decentralised-finance infrastructure on which the platform is built. Experimental and theoretical work on manipulation \citep{hanson2006manipulation,hanson2003combinatorial} and the documented episodes on Polymarket itself---concentrated position-taking in the 2024 election market and a disputed oracle resolution in March 2025---are discussed in Section~\ref{sec:conclusion}.