Suppose somebody did not have the time or resources to know about the different candidates and their proposed programs. What are the main disadvantages and possible advantages of random voting in such situations?
Assuming you mean voting for the random candidate:
You risk giving your vote to a truly awful candidate, one who you wouldn't have voted if you had even the barest facts.
Let's say candidate A proposes as his platform, making food (codenamed Soylent Blue) from human flesh; and to randomly infect people with dangerous diseases to promote medical scientific progress; and exterminate everyone whose first names start with letters K through T.
I suppose that you (independently of your leanings visavi real US politics) would never vote for such a candidate, yet random voting would indeed give such a candidate a strong chance of getting your vote.
It can amplify the perceived electoral mandate of a candidate you don't like, in certain scenarios.
E.g. as random numerical example, let's say you have 2 candidates, A who you would likely agree with, and B who you don't (but you're not informed enough to know that). There are 10 total electors, 2 for A, 4 for B, 2 abstaining (after reading the "disadvantages" list in this answer :) and one is yourself.
If you randomly vote and the random vote ends up for A, you didn't help A to win. If you don't vote, you didn't affect anything, and B wins with 40% votes, which is not generally considered a "mandate" as he got less than a majority of votes.
However, if you randomly vote and the random vote ends up for B, you raised their electoral share from 40% to 50%, which can be seen as a "mandate" because they got close to majority of voters. That means your random vote caused more damage to your interests than if you didn't vote at all, because the downside of random vote outcome for B far outweighs the upside of a random vote outcome for A.
Of course, if the candidate you prefer is currently winning the polls, this effect would be a benefit instead of a disadvantage to you, so in that scenario the effect would go to "Benefits" column.
If the party you would prefer is the party which typically benefits from higher voter turnout, you are hurting them, because your showing up for vote plays into their electoral modeling as a likelier vote for them (due to increased turnout), yet you are just as likely to vote for their opponent.
The harm isn't your vote, but you throwing off their models.
It makes campaigning efforts difficult for candidates, since their opinion polls and other advance indicators can't account for your vote in a predictable manner.
Whether this is is an advantage or a disadvantage can be argued both ways, so I'm calling it a wash.
If you value increased voter participation as a thing in and out of itself, voting randomly is a benefit vs. not voting.
As note in the first section, some of the disadvantages turn to advantages if the hypothetical situation is reversed (e.g. if the candidate you would have liked is already winning; or if your party is the party that benefits LESS from increased turnout).
If NOT voting has a tangible disadvantage (e.g, fines, prison, lack of being paid for voting, etc...); and voting non-randomly has a non-trivial cost (you need to spend a month studying entire 538 website), then voting randomly has a practical benefit of getting practical advantage of having voted (or removing practical disadvantage of not having voted), without incurring the cost of figuring out how to vote. (h/t Joel Harmon comment)
There are no advantages, and very few disadvantages
If your vote is truly random, your vote will be equally likely among all possible selections. Voting randomly cannot increase the likelihood of a good outcome, therefore it has no advantage over not voting.
Voting randomly will have little disadvantage with a large enough sample size. Consider a small state like Wyoming, which has a voter turnout of 170,000+.
Suppose Wyoming places an initiative on the ballot to kill all people named "John." (1.64% of people are named John). Suppose all people named John in Wyoming are highly motivated to vote against this initiative. Of the 431,434 eligible voters, 7,082 Johns will vote NO.
Let the remaining eligible voters vote randomly. The standard deviation is 325 votes. Meaning that 68.2% of the time, the YES vote will be within 325 votes of the mean. 95.4% of the time, the YES vote will be within two standard deviations of the mean and 99.7% of the time the YES vote will be within three standard deviations (i.e. 975 votes). The difference between the YES and NO is twice that, or 1950 votes. Still not enough to overcome a small percentage of people with overwhelming support.
Even for issues with a small split of 51%-to-49% and a voter turnout of 170,000, if even 25% of the population don't randomly vote, 21,675-vs-20,825 for a difference of 850, 95% of the time the random voters will have no effect on the election results.
It depends on what you consider to be beneficial. One of the reasons we have elections is because people disagree so strongly about how the government should behave. There are effects. For the effects to really matter we need to assume that it is not just you voting, but a large group of people all voting randomly. Keep in mind that for large numbers of random voters the distribution will tend to give all candidates nearly equal numbers of votes, so it isn't likely to sway an election.
Weaken the mandate. Suppose voters who care enough to learn prefer A over B with 60% for A and 40% for B. Now suppose half of all voters vote randomly. Instead of A winning 60% to 40%, A only wins 55% to 45%, making it harder to claim that the voters really really want A's policies. This can make it harder for A to make changes. If you are a conservative who believes in slow change or simply someone who doesn't like activist government this can be a good thing, but if you like an active government with clear purposes it is a bad thing.
In a very close election it could cause the less popular candidate to win. However in a close election that's not a terribly important concern. Either way about half of the voters will be happy and half will be upset by the outcome.
You make it harder for campaigns to predict voter behavior based on past elections. This can be a good thing because it may encourage them to be honest rather than making their lies fit their models. On the other hand it may prevent them from making their agenda fit citizens' desires.
You make it harder for the press to predict the outcome of the election. This could result in more people coming out to vote because the result isn't known ahead of time. Whether this is good or bad again depends on your POV. Less accurate predictions can also produce post-election unrest when a predicted winner unexpectedly loses and people suspect vote fraud or some other kind of stolen election.
You can - and do - get strange electoral outcomes with random voting
Australia, at least until very recent reforms, often has "accidental" candidates elected to the Australian senate on a very small number of votes. Until these reforms, it was very common for senators to elected when their party receives a very small number of primary votes. For example, Ricky Muir with 0.51%, or Steve Fielding with 1.9%).
The following graphic published on the ABC website shows the percentage of primary votes received by the party for each of the cross-bench (i.e. independents) senators in 2013.
Indeed, this can be partially attributed to "random voting". Donkey Votes are effectively expressing a random vote.
How is this possible?
- Single Transferable Vote electoral system
- Group Voting Ticket, where preferences are selected by the party where a voter chooses only one candidate; and
- Preference swap deals between minor parties.
A skilled preference negotiator such as famed "preference whisperer" Glenn Durery can exploit the system to produce outcomes where senators are elected on very small numbers of votes.
Can this be considered a benefit?
Maybe. Major party discipline in Australia is fierce, and having random Senators may allow legislation to be amended according to perspectives from outside of the major parties. YMMV as to whether this is a benefit.
If you vote slightly non-randomly, it's good enough.
Suppose there are two candidates - one is good, and one is evil. You didn't do any research, but you've heard enough through the odd news article and word-of-mouth that you have a 51% chance of voting for the good candidate.
Suppose there are 100000 voters and they all vote this way. The expected number of votes for the good candidate is 51000. The standard deviation of the same figure is 158.082 votes. In order for the evil candidate to win, the good candidate needs to receive less than 50000 votes, which will happen with a negligible probability of 0.0000000124%.