# Limits of Current US Prediction Markets (PredictIt Case Study)

(Dis­claimers: I work in the fi­nan­cial in­dus­try, though not in a way re­lated to pre­dic­tion mar­kets. Any­thing I write here is my opinion and not that of my em­ployer.
This is a US-cen­tric piece based on a case study of Pre­dic­tIt: as some peo­ple have pointed out in the com­ments be­low, if you are out­side the US you may have sub­stan­tially bet­ter op­tions.)

## SECTION I: INTRODUCTION

So there’s an ar­gu­ment that I’ve seen a lot over the past few years, par­tic­u­larly in LW-ad­ja­cent cir­cles, that goes some­thing like this:

You say you be­lieve X is likely to hap­pen. But pre­dic­tion mar­kets say X is likely not to hap­pen. Since mar­kets are effi­cient, you must be wrong. Or if you do know bet­ter than the mar­ket, why aren’t you rich? Since you haven’t bet on that mar­ket to make free money, you must be ly­ing. Or stupid. Or both!

This post is ded­i­cated to dis­agree­ing with that ar­gu­ment, not from an anti-Effi­cient-Mar­ket Hy­poth­e­sis po­si­tion, but from a pro-Effi­cient-Mar­ket Hy­poth­e­sis po­si­tion. My po­si­tion is:

The ar­gu­ment above is pretty much sound if we are dis­cussing main­stream fi­nan­cial mar­kets. If some­one claims to have bet­ter in­for­ma­tion than a main­stream fi­nan­cial mar­ket on the value of Google stock, or of cop­per, they ought to ei­ther use this knowl­edge to make a huge amount of money or stop talk­ing about it. How­ever, it is not true if we are dis­cussing pre­dic­tion mar­kets. Cur­rent pre­dic­tion mar­kets are so bad in so many differ­ent ways that it sim­ply is not sur­pris­ing for peo­ple to know bet­ter than them, and it of­ten is not pos­si­ble for peo­ple to make money from know­ing bet­ter.

I’ve been mean­ing to write this for a while, but got tipped over the edge by the re­cent post here, which talks about the limi­ta­tion of pre­dic­tion mar­kets be­ing the cor­re­la­tion of the events they pre­dict to other as­sets, and their con­se­quent value as hedg­ing in­stru­ments. That is...well...it’s not wrong ex­actly, but there are so many other prob­lems that are so much big­ger that I felt it was worth lay­ing (some of) them out.

Math fol­lows. I will be fo­cus­ing on Pre­dic­tIt for this anal­y­sis. Other pre­dic­tion mar­kets may work a bit differ­ently, but similar anal­y­sis is ap­pli­ca­ble to any of them. If you think the math is wrong I am happy to dis­cuss/​make changes, but I very much doubt any changes will ma­te­ri­ally al­ter the fi­nal mes­sage.

As of this writ­ing Pre­dic­tIt has Don­ald Trump at 40% to win the elec­tion (or, to put it an­other way, you can pay 40 cents for a share that pays out $1 if Trump wins). Sup­pose you think he is more/​less likely to win. How likely/​un­likely does it need to be for Trump to win for you to make money (in ex­pec­ta­tion)? Or, to put it an­other way, what range of prob­a­bil­ities for Trump to win are con­sis­tent with the pre­dic­tion mar­ket val­ues? ## SECTION II: REASONABLY SIMPLE PROBLEMS 1: Spread. This is only a small prob­lem, but it is non-zero. Pre­dic­tIt will sell me ‘Don­ald Trump wins’ shares for 40 cents, but will sell me ‘Don­ald Trump loses’ shares for 61 cents (which, from a fi­nance per­spec­tive, works out very similarly to let­ting me sell ‘Don­ald Trump wins’ shares for 39 cents). So if I think there is a 39.5% chance of Trump win­ning, there is no way for me to make money off of it: I can buy ‘Trump wins’ shares for 40 cents, or sell them for 39 cents, and if the true value is 39.5 cents both of these will lose me money. The range of pos­si­ble prob­a­bil­ities for which you can­not make money starts at 39-40%. 2: Trans­ac­tion Fees. Pre­dic­tIt charges a 10% fee on prof­its (see https://​​www.pre­dic­tit.org/​​sup­port/​​how-to-trade-on-pre­dic­tit). As far as I can tell, it does not net prof­its against losses be­fore calcu­lat­ing these fees. That is to say, if I make two$100 bets at even odds, win one, and lose the other, Pre­dic­tIt will charge me a $10 fee on my win­nings on the bet I won, even though over­all I have made no money. So if I think there is a 50% chance of Trump win­ning, and spend$100 buy­ing Trump Wins shares, in­stead of my ex­pected fi­nal money be­ing 50% * $250 =$125 for a $25 profit, my ex­pected fi­nal money is 50% * ($250 - $15 ) =$117.5 for a $17.50 profit. After ac­count­ing for this, the range of pos­si­ble prob­a­bil­ities for which you can­not make money is: 3: With­drawal Fees. When I ac­tu­ally at­tempt to with­draw my money from Pre­dic­tIt, Pre­dic­tIt charges an ad­di­tional 5% fee on the with­drawal, giv­ing me only 95% of my money back. How im­por­tant this fee is to any given bet varies de­pend­ing on how many bets I make on Pre­dic­tIt (if I am mak­ing mul­ti­ple bets with­out with­draw­ing money the effec­tive im­pact of the fee on any given bet is smaller), but for now let’s as­sume that (like most peo­ple) I do not have a Pre­dic­tIt ac­count and would need to cre­ate one to make this bet, and then with­draw my win­nings im­me­di­ately af­ter­wards. If so, my effec­tive win­nings shrink again as 5% of my money (not just my win­nings, all the money I de­posited) dis­ap­pears to Pre­dic­tIt. After ac­count­ing for this, the range of pos­si­ble prob­a­bil­ities for which you can­not make money is 4: In­vest­ment In­ter­est Rate/​Time Value of Money. The pres­i­den­tial elec­tion will not hap­pen un­til Novem­ber. Let us be gen­er­ous and as­sume that Pre­dic­tIt set­tles bets im­me­di­ately there­after (though their page for the bet states ‘Pre­dic­tIt may de­ter­mine how and when to set­tle the mar­ket based on all in­for­ma­tion available to Pre­dic­tIt at the rele­vant time’ and ‘Pre­dic­tIt’s de­ci­sions and de­ter­mi­na­tions un­der this rule shall be at Pre­dic­tIt’s sole dis­cre­tion and shall be fi­nal’). It is cur­rently July. That means it will be ~4 months un­til the bet re­solves, dur­ing which time your money will be tied up in Pre­dic­tIt. What else could you be do­ing with that money? Well, de­pend­ing on who you are, you could be get­ting rea­son­ably risk-free re­turns via e.g. Trea­suries or bank ac­counts, but those in­ter­est rates are low. On the other hand, your bet is de facto a loan to Pre­dic­tIt as well as what­ever bet you think you made. If Pre­dic­tIt sud­denly goes bankrupt in a mas­sive down­turn, or if who­ever runs it takes the money and flees to Dubai, you may not get paid back. So, what effec­tive in­ter­est rate would you charge to loan Pre­dic­tIt money in the cur­rent fi­nan­cial en­vi­ron­ment? How risky an in­vest­ment is it? If you would charge it 5% per year (which I don’t think is all that high by the stan­dards of bonds in risky com­pa­nies), then over those 4 months you could have made about 2% re­turn with­out the pre­dic­tion mar­ket in­volved. (Side note: this effect is larger or smaller de­pend­ing on what event you are con­sid­er­ing and how far in the fu­ture it lies. There’s some rea­son to ex­pect that this will make pre­dic­tion mar­kets a lit­tle more effi­cient as the event they per­tain to draws closer, but there are still quite a few other prob­lems). After ac­count­ing for this, the range of pos­si­ble prob­a­bil­ities for which you can­not make money is: So at this point, the 40% prob­a­bil­ity we see for Trump to win on Pre­dic­tIt is com­pletely com­pat­i­ble with any prob­a­bil­ity from 31.8%-45.7%. This is already...rather a wide range. And this is be­fore we en­counter two rather larger is­sues: ## SECTION III: HORRIBLE MESSY PROBLEMS 5: Taxes Note: I am not a lawyer! I am par­tic­u­larly not a tax lawyer! This sec­tion is spec­u­la­tive, even more US-cen­tric than the rest of this piece, may well be wrong, and even if it is right your tax situ­a­tion may be differ­ent! As far as I can tell, Pre­dic­tIt win­nings are treated by the US gov­ern­ment as in­come. This means two things: first, that if you win money on Pre­dic­tIt the US gov­ern­ment will tax it; and sec­ond, that if you lose money on Pre­dic­tIt the US gov­ern­ment will not let you net it against any­thing. So, just like Pre­dic­tIt’s fees did, taxes re­quire you to have a much higher chance of win­ning in or­der to be net-pos­i­tive. If you have a good ac­coun­tant and think you can net Pre­dic­tIt losses against an­other tax bill, or avoid pay­ing taxes on Pre­dic­tIt win­nings, this might not be ap­pli­ca­ble to you. If we as­sume you pay a 15% tax rate (ac­cord­ing to Google this is pretty close to the na­tion­wide av­er­age), the range of pos­si­ble prob­a­bil­ities for which you can­not make money is: And if we as­sume you are pay­ing 35% in­come tax (which re­quires a high salary, but I sus­pect a lot of the peo­ple who we’re hop­ing will come and cor­rect the pre­dic­tion mar­ket for us have high salaries...) then the range of pos­si­ble prob­a­bil­ities is: So now we’re fully com­pat­i­ble with Trump be­ing any­where from be­low a one-in-four to above a one-in-two chance! And then we en­counter the re­ally big one. 6: Bet­ting Limits Part of how mar­kets work is that peo­ple who know bet­ter will even­tu­ally be able to com­mand more of the money. If I am able to pre­dict the price of Ap­ple stock bet­ter than any­one else, I can mul­ti­ply my money faster, I can use my track record to get other peo­ple to in­vest with me, and I can di­rect large quan­tities of money, which both makes me a lot of money and al­lows me to move the mar­ket to a more ac­cu­rate val­u­a­tion. Pre­dic­tIt places a limit of$800 on your po­si­tion in any one bet.

At the mar­ket level, this means that you can no longer rely on small num­bers of in­tel­li­gent peo­ple to fix mar­ket prices for you. Since a small num­ber of in­tel­li­gent peo­ple can only mo­bi­lize at most $800 each, you are re­li­ant on lots of differ­ent peo­ple in­tel­li­gently pick­ing the right price. And at the in­di­vi­d­ual level, this makes it difficult to make any amount of money that mat­ters off a pre­dic­tion mar­ket. In a real fi­nan­cial mar­ket, peo­ple will in­vest large amounts of money. If a hedge fund pays ten mil­lion dol­lars a year hiring dozens of smart peo­ple to dis­cover a way of mak­ing 1% ex­cess re­turn, so long as they are in­vest­ing at least a billion dol­lars that is worth it. There­fore, in a real fi­nan­cial mar­ket, there is rea­son to ex­pect that any anal­y­sis that can cor­rect mar­ket prices will be done, even if it is difficult and ex­pen­sive to do. Pre­dic­tIt can just about man­age to let peo­ple who can cor­rect mar­ket prices make enough money to merit cre­at­ing an ac­count there. Re­call that, even with zero taxes, the range of pos­si­ble prob­a­bil­ities for which you could not make money was: But this is the range of prob­a­bil­ities for which you can­not make any money at all. Sup­pose that you think Trump’s chance to win is 50%. If you in­vest the max­i­mum$800, you will end up with in ex­pec­ta­tion:

which gives an ex­pected profit of about $75, and that was with­out con­sid­er­ing taxes. If you face a 35% tax rate, and think Trump’s chance to win is liter­ally zero, af­ter in­vest­ing$800 you end up with:

mak­ing a profit of about $250 in ex­change for know­ing with ab­solute cer­tainty that an event a pre­dic­tion mar­ket has at a 40% prob­a­bil­ity is guaran­teed not to hap­pen. This is not suffi­cient to merit ded­i­cat­ing time and effort to re­search. ## SECTION IV: CONCLUSION If some­one claims that they are ab­solutely cer­tain Trump will/​will not win the elec­tion, they should be able to make money on a pre­dic­tion mar­ket from this pre­dic­tion. How­ever, they may not be able to make very much money at all, and even if they are quite con­fi­dent that the pre­dic­tion mar­ket is wrong it may not be worth their time. As­sum­ing that this per­son should be will­ing to bet on their views on a pre­dic­tion mar­ket may be mer­ited, but even from a purely fi­nan­cial view it is a much closer af­fair than you may think. If some­one claims that Nate Silver and 538′s anal­y­sis team know bet­ter than a pre­dic­tion mar­ket what Trump’s odds of win­ning the elec­tion are, they are quite likely cor­rect. It is not pos­si­ble with pre­dic­tion mar­kets in their cur­rent state for them to make money from that knowl­edge. If you dis­miss this per­son be­cause they haven’t bet on pre­dic­tion mar­kets, you are ac­tively wrong, you are mak­ing me and a sys­tem I be­lieve is a good idea look bad by as­so­ci­a­tion, and I would like you to stop talk­ing about this. • I feel this is more “limits of Pre­dic­tIt” rather than “limits of pre­dic­tion mar­kets”. Do­ing the equiv­a­lent anal­y­sis for Bet­fair for some­one in the UK. (2% charge on prof­its, no fee for with­draw­ing). Right now the mar­ket for Trump to win is (£1200) 2.78 /​ 2.80 (£7421) Those im­ply prob­a­bil­ities of 35.97% and 35.71% After fees, 36.44% and 35.00%. That’s not a bad spread, and you can do this in much more size. (If you’re will­ing to work a bit, you can com­fortably get on £10,000s at pre­vailing lev­els). We pay no taxes on gam­bling, so there’s none of Sec­tion III to worry about. (Ad­mit­tedly, once we start talk­ing about even more se­ri­ous size we run into Bet­fair’s Premium Charge, but for your av­er­age UK based ra­tio­nal­ist, I don’t think Bet­fair is as bad a pre­dic­tion mar­ket as you’re mak­ing out). • It’s pos­si­ble! I’m writ­ing this from a very US-based per­spec­tive, where the main pre­dic­tion mar­kets I hear talked about are Pre­dic­tIt and IEM (and I think IEM might be even worse for bet­ting at scale?) If you have ac­cess to a pre­dic­tion mar­ket where these prob­lems are smaller/​nonex­is­tent, it will be more ac­cu­rate. And 2% charge of prof­its is much lower, plus look­ing quickly at the Bet­fair web­site it seems to have a pretty good amount of liquidity at a rea­son­ably small spread. I’m not sure how ac­cessible Bet­fair is to some­one from the US from a le­gal/​tax stand­point, so the over­all point may still stand if you’re talk­ing to some­one in the US/​if you think that a lot of the peo­ple in­formed on a given is­sue are in the US. (And do you re­ally have zero taxes on gam­bling prof­its? I would not have guessed that). • Yeah, the US has a bizarre tax sys­tem, and se­ri­ously pu­ri­tan laws about gam­bling (in­clud­ing treat­ing most non-reg­u­lated in­vest­ment re­turn as gam­bling). If one were se­ri­ous about this topic, the ob­vi­ous an­swer is to move some­place more rea­son­able (and then wait 10 years for the US to stop ex­pect­ing you to pay taxes on non-US ac­tivi­ties). At the very least, the good­ness of pre­dic­tion mar­kets in gen­eral should be stud­ied out­side the US, and a US-cen­tric post would be la­beled as “limits of bet­ting mar­kets in the US”. • Why don’t you con­sider this a big­ger ob­jec­tion to your post? IMO it’s ac­tu­ally very im­por­tant that a deep, liquid pre­dic­tion mar­ket with mil­lions of pounds of vol­ume and low fees ex­ists, and the prices are fairly similar to Pre­dic­tIt. IMO this is strong ev­i­dence that, in this case, PI’s prices aren’t be­ing dis­torted too much by the prob­lems you list. I be­lieve US-based bet­tors can get >1m USD on Trump or Bi­den at fairly close to Bet­fair odds with a lit­tle bit of time and pa­tience as well through var­i­ous means; I am aware of sev­eral peo­ple that have bet >$100k on the elec­tion and I think they could bet sub­stan­tially more if they want to. (some ex­am­ples of “var­i­ous means”: crypto ex­changes, find­ing e.g. poker play­ers who want to bet a lot on the elec­tion, find­ing a friend in the UK to bet on bet­fair for you)

• 1. I don’t agree that the prices are fairly similar. Pre­dic­tIt, poly.mar­ket, Omen, and FTX (let me know any other crypto ex­changes you want con­sid­ered) all have Trump ~40%. Bet­fair has him ~35%. I think that’s ma­te­ri­ally differ­ent. (Also, the vol­umes on those ex­changes are all pretty limited, so I’d be im­pressed if you could get $1mm down that way). I agree you could po­ten­tially get some risk down via P2P bet­ting, but I don’t think it’s fair to de­scribe that as a “pre­dic­tion mar­ket”. (Although it does nuke his point of ex­cus­ing peo­ple from not putting their money where their mouth is). 2. I don’t think you can get$1mm of risk down on Bet­fair. (Be­cause of the Premium Charge is­sue I men­tioned). I think the only way I can see that be­ing done at the mo­ment is P2P, and I’m not sure I’d be com­fortable with the coun­ter­party risk in­volved.

• Ac­cord­ing to Bet­fair you need to bet in over 250 mar­kets to trig­ger the pre­mium charge, and “Any sin­gle win that con­sti­tutes more than 50% of your gross prof­its over the life­time of your ac­count will be ex­cluded from the calcu­la­tion”. I think the hy­po­thet­i­cal per­son try­ing to bet $1m on the pres­i­den­tial race is safe. Re­gard­ing crypto, isn’t Augur v2 the­o­ret­i­cally sup­posed to launch soon? • Fair enough, for a one off it might work, al­though that wouldn’t be the case for some­one who is reg­u­larly ac­tive in pre­dic­tion mar­kets. The­o­ret­i­cally on the 28th, but that doesn’t an­swer my ques­tion about where you can cur­rently get se­ri­ous money down down in crypto? • I don’t know much about crypto, but I thought FTX was fairly liquid? I guess us­ing it is a le­gal grey area for US cit­i­zens though. From look­ing at the or­der­book it looks like you could get ~500k down over time with­out mov­ing the price by more than 5c. (I guess it de­pends on your defi­ni­tion of ac­cept­able slip­page; to me 5c is fine) • You were the one mak­ing the claims about crypto. FTX isn’t ac­cessible to US or UK based bet­tors for the Trump elec­tion. (So not a grey area, just not an area you can use at all). (I also re­fused to be­lieve that liquidity is real. When­ever I see or­ders like that in an or­der book I am usu­ally fairly con­fi­dent that there is some­thing sub­tle go­ing on which means they have a tech­nolog­i­cal way to avoid be­ing filled. Look­ing into FTX, the sub­tlty is that you can’t sub­mit or­ders 2% thru’ the or­der book, which means you can safely leave gi­gan­tic or­ders off-mar­ket to main­tain queue spot or for other tech­ni­cal rea­sons). • I know peo­ple liv­ing in the US have been able ot bet on FTX de­spite their ToS ban­ning US cit­i­zens; I haven’t done this so I don’t know the pro­cess. Maybe it’s straight up ille­gal rather than a le­gal grey area! (I think you might need to sup­ply fake KYC docs which does sound kind of ille­gal now that I think about it?) • Two replies here, I think: First, are any of the things you sug­gest in fact le­gal for US-based bet­tors? Se­cond, how difficult in terms of time/​in­con­ve­nience/​up-front cap­i­tal costs with­out the po­ten­tial for lev­er­age are they com­pared to the ways in which you can bet on e.g. the price of Google stock? If you’re tel­ling some­one in the US “you should be will­ing to bet your views on pre­dic­tion mar­kets, if you’re right it’s free money” when what you mean is “it’s free money pro­vided you’re will­ing to ded­i­cate hours to work­ing your money through crypto ex­changes, com­mit­ting tax fraud along the way”, that feels some­what differ­ent. I would be will­ing to tell some­one who thinks Google shares are un­der­priced “go buy some then,” be­cause buy­ing Google stock at low cost is le­gal, very easy, and even if you have limited up-front cash the real fi­nan­cial mar­kets offer op­por­tu­ni­ties for lev­er­age (op­tions etc.) I would not be will­ing to tell some­one who thinks Trump Wins shares are un­der­priced “go buy some then” when that pro­cess is time-con­sum­ing, difficult, and likely ille­gal. • Yes, it’s com­pletely le­gal for peo­ple in the US to bet on things; the only ille­gal part is be­ing an in­ter­me­di­ary. I see where you’re com­ing from re “you should be will­ing to bet your views”; I just want to be clear that if you think PI prices are in­effi­cient, it’s mostly not be­cause of trans­ac­tion fees/​taxes/​etc. How about tel­ling some­one who thinks Trump Wins shares are un­der­priced “go search on twit­ter and poker fo­rums for peo­ple bet­ting on this, and mes­sage a few of them”? This is com­pletely le­gal, doesn’t take that long, and is quite safe as long as you both agree to trust­wor­thy es­crow. There’s no guaran­tee you’ll find any­one will­ing to take your bet, but I think the chances you would are fairly high. • I don’t think that “lots of the in­formed peo­ple” be­ing el­se­where should make much differ­ence. The main met­ric for how se­ri­ously to con­sider data from pre­dic­tion mar­kets (in my mind) is open in­ter­est (or vol­ume /​ liquidity if open in­ter­est isn’t available). Yes—well, there are taxes on gam­bling prof­its, but on the bet­ting com­pa­nies, but not the in­di­vi­d­ual gam­blers. • First of all, I love this post, thanks for writ­ing it. That said, you have not at all made a case for this part: If some­one claims that Nate Silver and 538′s anal­y­sis team know bet­ter than a pre­dic­tion mar­ket what Trump’s odds of win­ning the elec­tion are, they are quite likely cor­rect. To make this case, it’s not suffi­cient to ar­gue that the bet­ting mar­ket’s im­plied prob­a­bil­ities are un­re­li­able. We also have to ar­gue that Silver & co are more re­li­able than the mar­ket. Per­son­ally, I’m still very skep­ti­cal of that—plac­ing money on a pre­dic­tion is a use­ful de­bi­as­ing tool even if the bet doesn’t pay for the anal­y­sis effort. Silver & co, on the other hand, at this point face ba­si­cally the same in­cen­tives as any other jour­nal­ists—not ex­actly a recipe for de­bi­as­ing! They’re go­ing to get very-fre­quent pos­i­tive feed­back when­ever their ar­ti­cles get clicks, ver­sus only a sin­gle burst of feed­back ev­ery four years on the ac­cu­racy of their mod­els. • Fair enough, that part is worded more strongly than I can re­ally jus­tify. I’d definitely still say it’s quite pos­si­ble that they are cor­rect, and I still wouldn’t think you can eas­ily show them to be wrong by EMH-style rea­son­ing. • I think one way of putting this is, given that a suc­cess­ful pre­dic­tion on Pre­dic­tIt only pays for a few hours of work and the 538 team pre­sum­ably has at least some full-time peo­ple, the 538 team has prob­a­bly spent more money in­ves­ti­gat­ing these ques­tions than the en­tire Pre­dic­tIt mar­ket com­bined. (How­ever, the in­cen­tives are differ­ent—a Pre­dic­tIt player has an in­cen­tive to be right but 538′s in­cen­tive is to tell a story that peo­ple who like read­ing about poli­ti­cal statis­tics will find plau­si­ble and in­ter­est­ing) • I think one way of putting this is, given that a suc­cess­ful pre­dic­tion on Pre­dic­tIt only pays for a few hours of work This is ex­tremely far off! I be­lieve on the or­der of 10-100 peo­ple on Pre­dic­tIt make over$100k/​yr, and if you’re already in­ter­ested in poli­tics sit­ting around bet­ting is a much eas­ier & en­joy­able way to spend an hour than most similarly paid work. (for refer­ence I’ve made around $30k in the last 5 months while os­ten­si­bly be­ing a full time stu­dent) • Can you clar­ify how this is pos­si­ble when the ar­ti­cle claims you can only make$100-200 per bet even if you have perfect cer­tainty? Do you just make tons of max value bets? I’m not sure how this site works ex­cept for what’s de­scribed in the ar­ti­cle.

• a lot of the costs in the ar­ti­cle are on net prof­its rather than gross prof­its (eg. taxes, with­drawal fees, risk of PI go­ing un­der). I didn’t in­clude taxes or with­drawal fees in that figure, but it doesn’t change the or­der of mag­ni­tude (and ofc it’s not clear yet what av­er­age tax rate I’ll pay this year)

• you can make far more on a con­tract by trad­ing on swings in ad­di­tion to wait­ing for the fi­nal out­come (e.g. buy “Yes” at 20c, sell at 80c, then buy “No” at 20c and sell it at 80c).

• There’s a large num­ber of con­tracts to trade on for a sin­gle im­por­tant event (e.g. to bet on Trump win­ning, you can bet $850 that Trump will win the pres­i­dency,$850 that a Repub­li­can will win the pres­i­dency, $850 that a Demo­crat will not win the pres­i­dency,$850 that Bi­den will not win the pres­i­dency, $850 that the next VP will be a man, and so on). They’re usu­ally not iden­ti­cal, but cor­re­lated strongly enough that you can get a lot of ex­po­sure to the event. There’s also brack­eted mar­kets on e.g. the mar­gin of vic­tory in an elec­tion, where each bracket (e.g. Dems win by 0-1%) is a sep­a­rate con­tract. A sin­gle MoV mar­ket might have 10 con­tracts, so you can bet thou­sands on it (and they tend to be volatile, so you can eas­ily have 5 figure to­tal turnover). Over­all, PI seems to be a biz­zare vi­o­la­tion of EMH where you can ex­tract large amounts of money for rel­a­tively lit­tle time/​low skill • This is a great post! As a costly sig­nal of me lik­ing it, I went in and fixed a bunch of for­mat­ting mis­takes and con­verted your equa­tions to nicely cen­tered LaTeX blocks. Do let me know if you pre­fer your ver­sion, and I am happy to re­vert it. • Ah, some­one with the time and en­ergy to proofread and LaTeX things for me! No ob­jec­tion, thank you very much! (I ac­tu­ally didn’t know other peo­ple were able to edit my posts though, how does that work?) • I am an ad­min on the site, so I can edit things (other users can’t). It’s always been pretty com­mon prac­tice on LessWrong for mods/​ad­mins to clean up bro­ken for­mat­ting, and it helps me feel the pain of the ways in which the ed­i­tor that I build causes prob­lems, so I feel more mo­ti­vated to fix them. • In around half of the equa­tions there is an ex­tra right paren­the­sis. It makes read­ing the equa­tions a bit ex­tra work as it changes the in­ter­pre­ta­tions some­what. In most of the equa­tions with an ex­tra right paren­the­sis, I be­lieve it is the left­most one (of the right paren­the­ses) that should be re­moved. • Oops, sorry, that is likely my fault. Will fix. (Edit: And I have now fixed it) • A few com­ments from some­one who reg­u­larly trades on Pre­dic­tIt: 1) The max­i­mum al­lowed bet is$850 (not $800), and this is only on a per con­tract ba­sis. There­fore, if you are bet­ting on Bi­den win­ning, you can max NO on Trump and YES on Bi­den for a to­tal of$1700 in the same mar­ket.

2) Pre­dic­tIt also has nu­mer­ous over­lap­ping mar­kets which are all tied to the re­sults of the gen­eral elec­tion. Cur­rently all the mar­kets be­low let you bet on the out­come in Novem­ber, al­low­ing your max bet in prac­tice to sub­stan­tially ex­ceed the $850 limit. https://​​www.pre­dic­tit.org/​​mar­kets/​​de­tail/​​3698/​​ https://​​www.pre­dic­tit.org/​​mar­kets/​​de­tail/​​5960/​​ https://​​www.pre­dic­tit.org/​​mar­kets/​​de­tail/​​5961/​​ ...and this doesn’t even in­clude state spe­cific mar­kets or mar­kets deal­ing with pop­u­lar and elec­toral vote mar­gins. 3) Many of the most suc­cess­ful play­ers on Pre­dic­tIt are ex­cel­lent at play­ing the swings. Sim­ply re­act­ing to news quickly can net you hun­dreds (or thou­sands) in min­utes, so there is of­ten no need to hold for long pe­ri­ods of time. Con­clu­sion: It is cer­tainly pos­si­ble for peo­ple to know bet­ter and also make a sub­stan­tial profit on Pre­dic­tIt. The$850 limit does im­pose a limit on prof­its for a sin­gle bet in a sin­gle mar­ket, but the wide se­lec­tion of mar­kets on the web­site al­low a ded­i­cated in­di­vi­d­ual to re­search and re­act their way to a prof­itable edge in vir­tu­ally ev­ery mar­ket, yield­ing good re­turns de­spite the fees. There is a very good rea­son the web­site has a ded­i­cated user base.

• Hey, I am in­ter­ested in cu­rat­ing this post, but do think it would be good for the ti­tle to be more ac­cu­rately scoped to be talk­ing about Pre­dic­tIt than all pre­dic­tion mar­kets. Some­thing like:

“How wide is the spread on pop­u­lar pre­dic­tion mar­kets? (Pre­dic­tIt case study)”

Or

“Limits of Pre­dic­tion Mar­kets (Pre­dic­tIt case study)”

would make me a bunch more com­fortable with cu­rat­ing it. Do you think that’s an op­tion?

• Sure, happy to change it. Does ‘Limits of cur­rent US Pre­dic­tion Mar­kets’ plus some com­men­tary at the top to the effect of ‘this is based on a case study of Pre­dic­tIt, per some com­ments if you are out­side the US you may have bet­ter op­tions’ sound rea­son­able?

• Yep, that sounds to­tally suffi­cient.

• A par­allel prob­lem with pre­dic­tion mar­kets: at non-fi­nan­cial-in­dus­try scales: they’re used as sig­nals of con­fi­dence. How of­ten do you see, af­ter some­one makes a bold claim, a re­sponse say­ing to “put your money where your mouth is.” But just the act of sig­nal­ling con­fi­dence can be in­trin­si­cally valuable to the per­son mak­ing a claim. In bet-capped places like pre­dic­tit, this can make equil­ibrium that are differ­ent from op­ti­mal, be­cause there are non-mon­e­tary in­cen­tives at work.

• To rea­son­ably con­clude that Pre­dic­tIt’s limits are “limits of pre­dic­tion mar­kets”—as your ti­tle as­serts—you need to show ei­ther that the other ex­ist­ing pre­dic­tion mar­kets also ex­hibit these limits, or that there is a fun­da­men­tal the­o­ret­i­cal rea­son for ex­pect­ing such limits to be ex­hibited by any pre­dic­tion mar­ket. As far as I can tell, you do nei­ther. (You do say that «similar anal­y­sis is ap­pli­ca­ble to any [pre­dic­tion mar­ket]», but you never jus­tify this as­ser­tion. In fact, of the six prob­lems you note, I think the only one that may be plau­si­bly claimed to be in­her­ent to pre­dic­tion mar­kets is #4, and even that one may be po­ten­tially solv­able.)

• Agreed − 4/​ is solved by al­low­ing mar­gin.

(Although mar­gin is trick­ier if the event can sud­denly re­solve to 0 or 1 at any time, I think there are even solu­tions to this)

• EDIT: NVM. This is just proof I didn’t get enough neona­tal io­dine.

For Sec­tion 2 on trans­ac­tion costs you write the calcu­la­tion for prob­a­bil­ity of win­ning is:

 100 /​ ( ( ( 100 /​ 0.40 ) * 0.9 ) + 10 )
Where does the ex­tra +10 come from?

EDIT: It’s so that you’re not pay­ing taxes on the amount of the origi­nal wa­ger.

max­i­mum_%_bet_on_P = bet_amount /​ (con­di­tional_win­nings—fees )

= bet_amount /​ (con­di­tional_win­nings(1-fee%) + bet_amount*fee%))

• The +10 is be­cause the 10% fee does not ap­ply to your origi­nal $100, only to prof­its. So if you would have$250 with­out the fee, rather than 250 * 0.9 = $225, you end up with$235.

• I think there are mis­placed paren­the­ses in your equa­tions. In sec­tion 3, they should be:

and so on in fu­ture equa­tions. Essen­tially the paren­the­ses should en­com­pass the +10 term as well in all your equa­tions. It seems your per­sonal calcu­la­tions were cor­rect be­cause the ac­tual prob­a­bil­ity bounds that you gave match up with this ver­sion of the equa­tion.

Thanks for an in-depth writeup!

• Should be fixed now, thanks for the heads-up!

• Pro­moted to cu­rated: I ex­pect I will be refer­enc­ing this posts quite a few times. I’ve re­peat­edly in the past done Fermi es­ti­mates of how big the spreads on the pop­u­lar pre­dic­tion mar­ket plat­forms is, and this feels like a more thor­ough ver­sion of that. Thank you!