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PoloHoleSet has an excellent answer. But I thought I'd mention one other bit that wasn't as prominently featured there:

Problems in a lottery tend to be for individuals and are resolved at the individual level ("My ticket won. Fix it"). The bulk of entrants has zero effect on the status of a winning ticket. There's a separate source of truth (the draw) that you're matching entries to.

Problems in an election tend to be over populations and cannot be resolved at the individual level ("My candidate didn't lose 25 000 to 25 004, they won 25 003 to 25 001 Fix it"). The bulk of entrants (votes) has a critical effect on the status of a winner. There's no way to resolve this issue by looking at one ballot. There's no separate source of truth, just an aggregate one.

States administer election rules and aggregation, but local municipalities handle voter registration, management of voting locations, and vote collection and tabulation. Each one can have their own separate rules or nuances, which have to conform to overall state regulation, but still allow for variation. With variation and lack of standardization, you get the possibility of variation and error in the process.

Lotteries generate revenue. A lot of revenue. As such, they are able to fund having uniform, standard, state of the art equipment and systems. Elections do not generate any revenue, and having the best equipment and systems is often seen as a luxury or largess. Machines are often old, malfunctioning, and there is a huge amount of variation within a state, let alone between states, in the types of machines that are used.

Lottery sales are pretty constant, and all the employees at outlets have to do is push a button on a machine and collect money. Election polling places are manned by volunteers who then have to answer questions in legal grey areas or help people with problems that exceed the volunteers' expertise or knowledge, and they have to call upon this expertise very infrequently, often for different types of elections when they do.

Elections are often managed by public officials whose continued success as public officials depends upon their systems not working optimally for selected portions of the population who are likely to vote against them. They have a vested interest in the elections not working properly for those selected populations. If I'm in charge of a system that I don't want to work optimally, it should not be surprising that the system does not work optimally.

Finally, a purchaser of a lottery ticket has zero personal input on the lottery ticket, itself. Yes, they often can choose their own numbers, but the ticket that is produced is a standard, controlled document that is produced by the system. If I mis-mark my number selection form, the ticket will reject, just like a ballot might, or it will record my input incorrectly on the produced ticket, just like a voting machine would. In this regard, it's not that different.

Those mistakes are more prominent in voting systems because each entry is noted and recorded. In a lottery system, it only becomes a large issue on a one in a hundreds of millions basis, and any kind of issue at all on a very infrequent basis, and mostly at a very trivial level. If there is a problem where I think my desires were not handled properly, my participation in the lottery is entirely discretionary on my part, subject to the terms and conditions set up by the lottery, so rejection of my complaints that my wishes were not properly followed allows for less recourse or potential mitigation than a system where I am exercising a fundamental right in society.

MegaMillions: How to Play (winning odds)

Powerball: Main Page (odds of winning link at bottom of page)

To sum up - there are vast differences between how the systems are set up and operate, and to the degree that they are similar in important ways, the frequency problems are noticed and importance of problems, between the systems, is also different.

There's not a lot that is equivalent or comparable there.

Lotteries and elections differ in one crucial respect: lotteries validate a small number of winning tickets in an easily verifiable way: either the ticket is legitimate or not, and its either a winner or it isn't. You can verify whether a lottery ticket is a winner or not independent of the other lottery tickets sold. The Powerball states can sell a billion (or more) tickets without increasing their cost of validating the winners substantially.

With elections, you have to validate that every ballot cast is legitimate before you can determine (with certainty) who won the election.

Imagine a lottery in which all people who buy tickets check off a red box or a blue box, and the color that gets checked off most pays off a prize to all people who have a ticket with that color checked off. The lottery officials have to count the individual tickets to see which color won before they can pay out, and you can bet that the ticket holders would raise a stink if the margin of victory for one color was small. To paraphrase @BowlOfRed's answer: "My color didn't lose 25 000 to 25 004, it won 25 003 to 25 001! Fix it!"

When doing something consistently, weekly, after some time you work out all the kinks, and system works like well oiled machine.

If you do something every other year, with volunteers, some of them new new and never done it, and with law and/or technology possibly changed from the one used previous time - you are doing it for the first time, going live with little preparation. In such situation, Murphy's law applies with the full strength: anything that can go wrong, will (in some of the places).

If we had elections every week, like lottery does, glitches will be eventually worked out (but turnout would be abysmal :-) )

In addition to other fine answers:

If people lose faith in the lottery...

then ticket sales will fall, tax revenues will drop, and the persons running the lottery will be replaced.

If people lose faith in elections...

fewer votes will be cast, political elites will gain even more power, and the persons running the election will keep their jobs.

So OP, don't lose faith in elections.

A few things that I don't see being answered in other answers make elections very complicated, and these are the things that delay results:

Mail-in ballots I'm not sure how it works in other jurisdictions, but in mine (Dallas County, TX), when you mail in an absentee ballot, you fill in your ballot, put it in an envelope with no markings on it. Then you put that envelope in a second envelope that has your information, information about your ballot request (barcoded) and your signature on it. On election day, the outer envelopes are checked (to make sure that the information is on the up-and-up) and that you didn't also vote in early voting or on election day). Then the envelope is emptied putting its contents (the inner envelope in a separate bin). Once that step is done, then the inner envelopes are emptied and the ballots are counted. This assures anonymity during the actual counting. This is my understanding, not the documented procedure. In some jurisdictions (like Oregon), all ballots are mail-in. In others (CA and AZ, for example), there's a substantial percentage of ballots that are mailed-in.

Deadlines In some jurisdictions, mail-in ballots must be received by election day. In others, they must be postmarked by election day. In Florida, for example, overseas and military mail-in ballots can be received up until Nov. 16 (Friday). You don't normally see this as a delay in "calling the winner" because usually, the margin of victory is such that everyone knows that the mail-in ballots will not affect the eventual outcome. However, in just about every jurisdiction, the final published vote totals differ significantly from the day-after-the-election totals. However these differences don't generally affect the overall outcome.

Provisional Ballots If there is a hang-up at the voting booth (for example, a question about voter ID), the voter may cast a Provisional Ballot. They have a similar two envelope system to mail-in ballots. Sometimes, it's the voter's responsibility to cure the hang-up. In any case there is usually a specified time period for these things to get settled.

Insane Politics Lawyers are everywhere and the stakes are high. Candidates will file suit for just about any cause. Look at how easy it was to setup the Florida recount this year. In 2000 it went all the way to the Supreme Court. As part of this process, PR folks on the candidates team send out messages that the elections office is run by idiots and the other candidates team is made up of scurrilous cheaters.

All in all, the 95% of ballots that follow the standard process get processed (and recounted) easily. However, if there's only a 0.5% difference between the candidates, the edge cases predominate. There are no edge cases with lotteries (in general).

I have worked in the election field in New York and I believe I pick up a lot of info listening to the news because of it.

First I would challenge your statement and ask for you to provide valid, credible sources.

And yet miscounting the votes seems to happen on a mass scale.

Next I would say that lottery tickets are much simpler than election ballots. If you look at how many different ballots are available in a particular state you will see that it is at least 100:1 in terms of permutations.

Then you can look at how lottery works. It is tightly controlled, nobody has a right to play and you pay money for a ticket. You can also play as many tickets as you please. Compare that to voting where many people have the right to vote and depending on the jurisdiction the ability to register to vote is much more lax than buying lottery tickets.

If I had a choice to administer a 50 lottery systems vs an election system in one state I would choose lottery all day long.

I could add more but those details are somewhat covered in other answers. I believe what I have stated should make clear

Why is counting election totals more difficult than lottery
administration?

Fourth, the scale at which lotteries are administered is a few orders of magnitude more sophisticated than the voting. Some states have weekly lottery drawings. Whereas votes only happen every 2 years.

This is a key factor (ability to get things right v.s. likelihood of mistakes).

Lotteries are a permanent, ongoing operation happening all the time, which warrants full-time staffing of management/oversight positions. Sales of tickets, drawings of winning numbers, payment of prizes, distribution/maintenance of equipment, printing/shipping/sale of scratch tickets, etc. are happening every day (or close to it) on an ongoing basis. You can hire people to do these jobs. They can continue to do these jobs for a long time.

Elections happen once every four (or two) years (or more frequently, depending on local laws/processes). It's highly unlikely anyone will be printing and distributing ballots, operating a polling location, or counting votes in March 2019 (barring any special elections). There are various types of oversight (depends on city/town/county/state etc.), some of which are permanent, long-term employees, and some of which are elected officials (who may change due to execution of an election, and may have a vested interest in non-legitimate outcomes), but you can't really hire a full-time ballot counter (or ballot printer, or voting location staff), unless you want to waste a lot of money paying them when there is no election.

Public reporting/discussion/opinion is another factor.

Lotteries are generally self-funded revenue generators, and the only people affected by them are those that choose to participate (can't lose if you don't play). Lottery fraud can and does happen ^{(citation needed - there've been a few pretty public cases)}, but a lot of people just don't really care, because it doesn't affect them.

On the other hand, elections can affect everyone, so the general public has a vested interest in the outcome. If the election results in a particular law going into effect (either directly by ballot measure, or indirectly by electing officials who put it in place), everyone is subject to that law, regardless of whether or how they voted. This leads to more coverage and public discussion of any election issues.

Anonymity

Many (most?) U.S. states do not allow anonymous lottery winners; winners' names are public information. Votes are completely anonymous. My polling location will have a record that I showed up, received a ballot, and placed a ballot into the ballot machine. There is no record of how I voted, or which races I did or did not vote in. There is no way to verify that my vote in particular was counted, other than a verification that all votes cast at my location are accounted for.

The other aspect of the Lottery not mentioned is that the winning ticket is a bearer item, meaning that the identity of the winner is only tied to the individual who's name is on it. Find a stray ticket with the winning number of the big jackpot in the gutter? It doesn't have anyone's name signed to it... You're even luckier than the guy who purchased a winning ticket!

Ballots are anonymous for various good reasons, but that causes a lot of problems when you have to validate the ballot as legitiment or not... the 2000 problem from Florida was attributed to "Hanging Chad" where the hole punch removed the paper in such a way that the whole damaged both check boxes and with no way to tell who the voter actually wanted, it became a big fight over what to do with the ballots... cast them for candidate A, candidate B, or invalidate someone's vote?

1. Elections are more complicated than lotteries. I don't play the lottery to excuse me if I'm missing some details, but a quick check of my state's lottery web site shows 10 kinds of ticket you can buy: Powerball, Pick 3, Pick 4, etc. In each case, you either choose or are assigned between 3 and 6 numbers.

Compare that to a voting ballot. In the last election, my ballot listed at least 13 races: federal senate, state senate, federal house, state house, governor, state treasurer, secretary of state, state supreme court judge, county probate judge, municipal judge, regents of the state university, board of the county community college, county commissioner, maybe others that I'm forgetting, not to mention 3 proposed amendments to the state constitution. This information has to be pulled together from federal, state, county, and city sources. Different races appear on different ballots: I can vote for mayor of my city but not for mayor of a neighboring city. People in different districts have different choices for house and senate. Etc. In some races there is one winner. In other races there are several winners, e.g. for the state supreme court we were electing 2 judges, so the top 2 vote-getters won.

2. With a lottery, the people who run the lottery get to make up the rules, and they can invent rules that make it easier to administer. (I suppose if they made rules that were too obviously biased, like "relatives of members of the lottery commission get 2 chances to win while everyone else only gets 1", the state would step in.) The people who run elections can't make up rules to make their lives easier. For example, the lottery people can say that you pick numbers from the range 1 to 60. If someone said that they want to chose 61, the lottery people can just say "no, that's not a choice", and that would be the end of it. But the election people can't say, "you must choose Democrat or Republican, and letting you pick Libertarian or Green Party is just too complicated".

Likewise, the lottery people have an easy way to control who plays: You have to pay for a ticket. If you want another ticket, fine, pay for another ticket. They don't have to worry about who is allowed to buy tickets or making sure no one buys more than one ticket. They don't have to verify your identity when you buy a ticket. Etc.

It's much more complicated with elections. Some people are allowed to vote and some aren't. Each person is only allowed to vote once. You don't pay to vote so the only disincentive to illegal voting or multiple voting is getting caught and prosecuted.

3. People who run the lottery don't generally care who wins. They have zero incentive to cheat to let one stranger win over some other stranger. They might conceivably cheat to help a friend or relative win, but that would be instantly suspicious -- if the lottery commissioner's brother-in-law wins a $50 million jackpot, I'm sure someone would investigate. (I'd hope so, anyway.)

People who run elections often care a great deal about who wins. While one would hope that their highest ideal is fair elections, it doesn't take incredible cynicism to wonder if some election officials might not try to stack the deck now and then for their preferred candidate. As every candidate is favored by large numbers of people, you can rarely say, "wow, it was awfully suspicious that this candidate won".

4. The Lottery has a strong institutional incentive to be fair and accurate. If there is evidence that the games are biased -- or even rumors -- people will refuse to play and the lottery will go broke. But with elections, it's the only game in town. Sure, if you discover that elections are biased, you can refuse to vote. But then you've given up your chance to influence the political process. The people who run the elections don't lose: you do.




5. As others have noted, lotteries are relatively easy to verify. If someone claims to have the winning ticket, you check that one ticket and say yes or no. You don't need to re-check every other ticket that was sold. If there's serious question that the ticket was forged or some such, you can devote considerable resources to investigating it. With elections, you have to study every vote. If someone won the election by just one vote, you can't say, "oh, it was Fred Smith who cast the deciding vote, so let's make absolutely sure that we know who Fred Smith voted for". EVERYONE cast the deciding vote. If any one of all those millions of ballots was illegally cast or was miscounted, then the election results could be wrong.