随着从单个候选人到公投议案各类事件均设市场,预测市场平台卡尔希(Kalshi)的交易员共完成了超过25亿美元的交易,试图将自己对选举的洞察转化为利润。
该公司表示,这一金额几乎是2024年大选相关市场交易额的两倍。根据哥伦比亚广播公司新闻(CBS News)对选举前一周市场赔率的分析,卡尔希市场看好的候选人在95%的国会或州长中期选举中最终胜出。
专家指出,选举市场能猜对众多 race 是因为参与人数众多,且交易时可依托高质量信息。
达特茅斯学院经济学教授埃里克·齐泽维茨(Eric Zitzewitz)表示:“这些是我们有史以来规模最大、流动性最强的选举预测市场。”他研究政治预测市场已有历史,可追溯至1880年。
他在选举后回复CBS News时写道:“它们的校准度相当高,这并不意外。”
卡尔希用户交易的是关于事件是否发生的“是或否”问题,公司则通过每笔交易的手续费盈利。例如,若有人以67美分的价格购买“是”的期权,认定阿卜杜勒-埃尔·赛义德(Abdul El-Sayed)会赢得密歇根州参议院席位,那么他们将获利33美分——这些价格表明,当时市场认为赛义德有三分之二的胜率。
以下是卡尔希选举市场与最终结果的对应情况。部分竞选因CBS News在报道发布时尚未预测出胜者而被排除在外。CBS News与卡尔希存在合作关系,卡尔希赞助了CBS News今年选举报道中对其预测市场数据的使用。本次分析独立于该合作关系开展。
看好的候选人在95%的众议院竞选、91%的参议院竞选以及97%的州长竞选中胜出。
平均而言,交易员认为最终胜选者有91%的概率胜出。不少中期选举竞争并不激烈,这也是为何卡尔希上多数胜选者的赔率达90%或更高。
被看好的候选人在23场竞选中失利。在所有这些竞选里,交易员都看好共和党候选人,但最终是民主党候选人获胜。南卡罗来纳州参议院竞选是最大意外之一,当时卡尔希交易员给胜出者安妮·安德鲁斯(Annie Andrews)的胜率仅为23%。德州州长竞选中,击败现任州长格雷格·阿博特(Greg Abbott)的吉娜·伊诺霍萨(Gina Hinojosa),在卡尔希上的胜率标价为33%。
为验证卡尔希市场是否达到研究人员所称的“良好校准”状态,我们可以根据卡尔希交易员对每场竞选给出的概率,将竞选划分为不同组别并计算平均值。在一个校准合理的市场中,胜率为60%的候选人应当有60%的获胜概率。
随后我们可以将其与这类热门候选人的实际胜选比例进行对比。
在所有“稳胜”竞选中,热门候选人都胜出了,尽管部分竞选中的赔率显示少数热门候选人可能落败(赔率上限为99%)。
同样,在“大概率”区间标价的候选人胜选频率略高于卡尔希概率的预测结果。
此前对预测市场的研究表明,这些市场更常偏向热门候选人,其程度超过价格所显示的情况。这一现象被称为热门-长射偏差:交易员认为爆冷候选人的实际胜算高于真实情况,从而压低热门候选人的价格。
但在热门候选人优势不明显的中期选举中,标价较高的候选人胜选频率低于预期——意味着这些市场并未偏向支持热门候选人。
验证这类预测市场的准确性需要假设每场竞选的结果相互独立,但实际情况并非如此。
“如果大量选民转投民主党,那么所有民主党候选人的胜选概率都会更高,”爱荷华大学金融学教授汤姆·里茨(Tom Rietz)在选举前表示。里茨负责运营爱荷华电子市场,这是一个自1988年起存在的学术预测市场。
选举前一周,卡尔希市场预测民主党将赢得56.7%的国会和州长席位。这些候选人最终的胜选率为60.4%,略高于市场预测值。
卡尔希发言人伊丽莎白·戴安娜(Elisabeth Diana)告诉CBS News:“大家都低估了民主党。与其他任何专业预测模型相比,卡尔希对民主党的低估幅度最小。”
但数据显示情况并非如此。尽管卡尔希的准确性随着选举日临近而提高,但《纽约时报》的分析发现,在选举周期的大部分时间里,卡尔希的表现落后于其他预测模型,包括政治统计学家内特·西尔弗(Nate Silver)的模型。
虽然卡尔希这类预测市场声称比民调更准确,但优质的民调信息有助于预测市场提高准确性,因为交易员会依托民调进行交易。
齐泽维茨表示:“预测市场需要基本素材,而选举中的基本素材就是民调。”
但里茨指出:“民调只是一条信息。市场中的交易员可以获取全球范围的各类信息。”
当拥有优质信息的用户发现市场可能与现实不符的机会时,他们会有动力进行交易。他们对某一候选人或竞选的单笔交易有助于推动市场向更现实的赔率靠拢。
都柏林大学学院研究经济预测和预测市场的经济学助理教授康斯坦丁·布尔吉(Constantin Burgi)表示:“如果出现新的信息,而市场价格并不合理,就会有人试图通过这种方式赚钱。”
这会给普通交易员带来损失。越来越多的专业交易员——包括华尔街的大型机构——正在参与预测市场。此前的分析发现,在预测市场中交易的多数人会亏损。
布尔吉表示:“我们知道很多人想要赌博,很多人会因此亏损,甚至可能上瘾。但对我们这些旁观者来说,这是惊人的数据。”
他补充道:“那些使用和研究数据的人与参与交易的人之间的这种矛盾,我认为将成为未来几年的重大问题之一。”
数据来源说明
本文中,CBS News分析了卡尔希的481场国会和州州长竞选数据,CBS News于东部时间周一晚上10点预测出这些竞选的胜者。每场竞选设有多个市场,每位候选人对应一个“是/否”选项。CBS News分析了胜率最高候选人的市场数据,即本文章中所指的交易员看好的候选人。对于每位候选人,CBS News记录了选举前7天(10月28日)东部时间午夜前的最后交易价格。若当日无交易,则使用之前最近的交易价格。
为确定市场校准度,CBS News采用卡尔希的赔率划分标准,将竞选分为“稳胜”“大概率”“倾向”和“势均力敌”四个类别。由于“势均力敌”和“倾向”类别的竞选数量过少,我们将这两个类别合并,以扩大样本量。
制作人员
报道与分析:朱莉娅·英格拉姆(Julia Ingram)、玛德琳·梅(Madeleine May);设计与开发:朱莉娅·英格拉姆(Julia Ingram)、格蕾丝·曼泰(Grace Manthey);编辑:格蕾丝·曼泰(Grace Manthey)、妮可·蔡(Nicole Chau)、马修·莫斯科(Matthew Mosk)。
With markets on everything from individual candidates to ballot measures, traders on the prediction market Kalshi exchanged more than $2.5 billion seeking to turn their election smarts into profit.
That sum was almost double the amount traded in markets on the 2024 general election, the company said. Ultimately, the candidates who Kalshi markets favored won 95% of congressional or gubernatorial midterm races, according to a CBS News analysis of market odds from a week before the election.
Experts say that the election markets get so many races right because of the large volume of people participating, and the availability of high-quality information to base trades on.
“These are the biggest, most liquid prediction election markets we’ve ever had,” said Eric Zitzewitz, an economics professor at Dartmouth College who has studied political prediction markets dating back to 1880.
“It is no surprise that they were quite well calibrated,” he wrote to CBS News following the election.
Kalshi users trade on yes-or-no questions about whether an event will occur, and the company makes money on transaction fees for each purchase. For example, if someone bought a “yes” that Abdul El-Sayed would win Michigan’s Senate race when that side was trading at 67 cents, they profited 33 cents. Those prices suggested the market believed El-Sayed had a two-thirds chance of winning at that time.
Here’s how Kalshi’s election markets lined up with the results. Some races were excluded because CBS News had not projected a winner by the time of publication. CBS News has a partnership with Kalshi, which sponsored the use of its prediction market data in CBS News election coverage this year. This analysis was conducted independently of that partnership.
The favored candidate won in 95% of House races, 91% of Senate races, and 97% of governor’s races.
On average, traders gave the eventual winner a 91% chance of coming out on top. Many of the midterm races weren’t competitive, which is why so many of the winners’ odds were 90% or higher on Kalshi.
The favored candidate lost in 23 races. In all those races, traders favored Republican candidates, and Democrats won instead. The South Carolina Senate race was one of the biggest upsets, with Kalshi traders giving winner Annie Andrews a 23% chance. Traders priced Gina Hinojosa, who beat incumbent Greg Abbott in the Texas governor race, at a 33% chance.
To test whether Kalshi’s market is what researchers call “well-calibrated,” we can split races into buckets based on the probability Kalshi traders gave each race and average them. In a calibrated market, candidates with 60% odds should win 60% of the time.
Then we can compare that to the percentage of races where those favorites won.
The favored candidate won in all safe races, though the odds suggested a few would lose. (Odds are capped at 99%.)
Similarly, the candidate priced in the “likely” range won a bit more often than the Kalshi probabilities forecasted.
Previous research on prediction markets shows that they settle for the favored side more often than the prices suggest they would. This is called favorite-longshot bias: Traders believe the underdog has a greater chance than they actually do, pushing down the price of the favorite.
But in midterm races where the favorite was less clear, the higher-priced candidate won less often than anticipated — meaning the markets weren’t biased in their favor.
Testing the accuracy of prediction markets like this assumes that each race’s outcome is independent, which isn’t the case in reality.
“If lots of people turn out [to vote] for the Democrats, then all of the Democrats are more likely to win,” said Tom Rietz, a finance professor at the University of Iowa, before the election. Rietz helps run the Iowa Electronic Markets, an academic prediction market that has been around since 1988.
A week before the election, Kalshi markets forecast Democrats would win 56.7% of congressional and gubernatorial races. These candidates ended up winning 60.4% of the time — slightly more than the markets predicted.
“Everyone underestimated Democrats,” Kalshi spokesperson Elisabeth Diana told CBS News. “Kalshi underestimated them less than any other professional forecaster model.”
But the data suggests otherwise. While Kalshi’s accuracy improved as Election Day drew closer, a New York Times analysis found that it lagged behind other forecasting models, including the one from political statistician Nate Silver, for most of the election cycle.
While prediction markets like Kalshi claim to be more accurate than polls, good polling information helps prediction markets become more accurate, because traders rely on polls to make their trades.
“Prediction markets need raw material to work with and polling is the raw material when we’re talking about elections,” Zitzewitz said.
But “a poll is one piece of information,” Rietz said. “The traders in the market have access to the entire world’s worth of information.”
And users who have good information are incentivized to trade when they see an opportunity where markets might not match reality. The individual purchases they make on a candidate or race can help push the market toward more realistic odds.
“If there’s any new information coming and the price is not what it should be, there’s some people that race and try to make some money there,” said Constantin Burgi, an assistant economics professor at University College Dublin who studies economic forecasts and prediction markets.
That comes at a cost to the average trader. Increasingly, professional traders — including major Wall Street firms —are participating in prediction markets. Previous analyses have found that the majority of those who trade in prediction markets lose money.
“We know that lots of people want to gamble, lots of people will lose money with that and might be addicted to it,” Burgi said. “But for us as the outsiders looking at this, this is amazing data.”
“That conflict between the people using the data and looking at the data versus people participating in it, I think that will become one of the big questions over the next couple of years,” he added.
About the data
For this article, CBS News analyzed Kalshi data for 481 congressional and state governor races for which the news organization had projected a winner by 10 p.m. Eastern Time on Monday. Each race has multiple markets, with a yes/no side for each candidate. CBS News analyzed the data in the market for the candidate with the highest chance of winning, or highest “yes” price, referred to in this article as the traders’ favorite. For each candidate, CBS News recorded the last trading price before midnight Eastern on Oct. 28, seven days before Election Day. If there was no trading that day, the most recent trade price before that was used.
To determine market calibration, CBS News adapted Kalshi’s odds cutoffs for “safe,” “likely,” “lean” and “toss-up” races. Because there were so few tossup and leaning races, those two bands were combined for a bigger sample.
Credits
Reporting and analysis by Julia Ingram and Madeleine May. Design and development by Julia Ingram and Grace Manthey. Editing by Grace Manthey, Nicole Chau and Matthew Mosk.
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