How many up-votes does an answer need for those up-votes to be statistically significant?
On getting the views and votes, and what do they mean ...
Many factors affect votes:
The season, holidays, day of the week, time of day, current events (school, sports on TV, national fireworks celebrations, big news, etc.), even disasters and connectivity.
On an inactive site most of the active members may get to see the question and it's answers over a period of a week or two, negating many of the above effects.
On a busy site the question may be pushed down the list, especially if it gets downvotes and one fast answer (for an Enlightened badge, or an Explainer, Refiner, or Illuminator badge, or the Lifejacket, Lifeboat, and possibly the Guru badge); with one quite good answer that is doing well others may be discouraged to enter a race where another answer has a head start.
Viewers may be attracted by the title of the question, the tags, and first two sentences (when they can see them), even the user's name and reputation. Votes, number of answers, views and status [Open/Closed] may also affect future visits. To vote one must visit, questions that don't attract views can't receive votes. Under certain circumstances a question may enter the Hot Network Question list, though not all sites gain such exposure; the result of such exposure varies enormously.
This is what your question looks like:
All of the above, and anything I missed, affects receiving a visit (and a potential vote).
Having arrived at the question, since you ask only about votes on answers, it requires at least one clear answer that tackles the question well. Since you only ask about "vote number per view count" (to determine "answer quality") the answer doesn't need to be complete or great, it only needs to seem OK and be favorably received. The Bandwagon Effect can come into play, in many flavours.
[Note: Those aren't my standards, they seem to be what is proposed by your question.]
Voting in political science has what is called: "input, output and throughput legitimacy", "negative and positive legitimacy", and "instrumental and substantive legitimacy".
Those are:
Whom can vote and how: (reputation: 15 vote up, 100 vote down (and at a cost of 1 reputation, the loss of the vote down privilege), 1000 see up and down vote counts, instead of the total aggregate. The "throughput legitimacy" can refer to both correct counting of votes, and more frequently voting reversals.
Negative legitimacy refers to people studying the question and answer and voting correctly while positive legitimacy refers to people holding
appropriate tag badges.
The instrumental legitimacy is the availability of an expert on the subject to answer your question (regardless of reputation, tags, votes), while the substantive legitimacy is people's (including the author's) belief that the author provides a defining answer. If someone wrote a book or paper about which you are asking that often becomes the case, but even Einstein made mistakes.
It's more than simply ability and motivation, turnout decisions and the quality of vote choice. Great questions (and their answers) can have few or a lot of views, while good or bad answers can have many up or down votes, even none. If a team of experts doesn't double check each Q&A then you need to do your own research/homework once you have a hint unless what is written is obviously correct.
See the Dempster–Shafer theory:
"Belief functions base degrees of belief (or confidence, or trust) for one question on the probabilities for a related question. The degrees of belief themselves may or may not have the mathematical properties of probabilities; how much they differ depends on how closely the two questions are related. Put another way, it is a way of representing epistemic plausibilities but it can yield answers that contradict those arrived at using probability theory.".
More votes (up or down) from more people doesn't make something more correct or incorrect, it simply moves the line from zero up or down; unless every vote is correct.
In the paper: "Assessing the reliability of crowdsourced labels via
Twitter" (.PDF), by Noor Jamaludeen, Vishnu Unnikrishnan, Maya S. Sekeran, Majed Ali, Le Anh Trang, and Myra Spiliopoulou they write:
"We propose a new annotation tool for tweet sentiment labeling, that capitalizes on topic-specific expertise of Twitter users. We derive topics from the tweets and use them to derive topic-based reliability scores
for the annotators. These scores we use in a weighting scheme for the annotated tweets. This allows us to exploit the fact that an annotator may be more reliable for tweets belonging to a certain topic than to other topics. ... We compare our model with Kappa Weighted Voting and Majority Voting as baseline methods, and show that our approach performs well and is robust when up to 30% of the annotators is not reliable.".
As explained in the first half of this answer Stack Exchange doesn't use voter reliability or tag expertise, the ability to vote is strictly privilege based. Sometimes you simply need to assess the author and decide if it's worth the time and effort to confirm their answer, no one is required to do that before they vote; but you may need to do that before you rely on the answer.
Can I rely on an answer with one up-vote? And with 100 up-votes? If they're different, where's the line? What if the question has a small number of views? Do the answers to the above change?
Sometimes only ~10% of the views will be accompanied by upvotes without any downvotes, and often that is an indicator that the answer is correct, but it would be foolish to apply anything as a indicator of certainty.
And related: What is a statistically significant number of down-votes?
Sometimes if there's ~10% downvotes compared to upvotes that indicates some problem, but darned if you could spot it if you don't know the answer; it's also possible for those votes to be incorrect (or from competitive answerers).
An answer with a few downvotes and no upvotes can be correct, even accepted.
The badges Tenacious and Unsung Hero are awarded for zero score answers. Some sites, such as here or Space.SE, have awarded zero of those badges while other sites, such as Physics.SE (220) or Chemistry.SE (12) have a small number of those badges awarded. On Stack Overflow they've awarded 78.3K of those badges. At the same time, accepted answers can clearly be wrong.
Condorcet's jury theorem explains:
"The assumptions of the simplest version of the theorem are that a group wishes to reach a decision by majority vote. One of the two outcomes of the vote is correct, and each voter has an independent probability p of voting for the correct decision. The theorem asks how many voters we should include in the group. The result depends on whether p is greater than or less than 1/2:
1. If p is greater than 1/2 (each voter is more likely to vote correctly), then
adding more voters increases the probability that the majority decision is
correct. In the limit, the probability that the majority votes correctly
approaches 1 as the number of voters increases.
2. On the other hand, if p is less than 1/2 (each voter is more likely to vote
incorrectly), then adding more voters makes things worse: the optimal jury
consists of a single voter.".
In the paper: "Measuring Voter Decision Strategies in Political Behavior and Public Opinion Research" (22 Mar 2018), by Richard R Lau, Mona S Kleinberg, and Tessa M Ditonto, in the AAPOR journal "Public Opinion Quarterly", Volume 82, Issue S1, 2018, Pages 911–936, they write:
"Broadly speaking, a decision strategy is “a set of mental and physical operations that an individual uses to reach a decision” (Lau and Redlawsk 2006, p. 30; see also Payne, Bettman, and Johnson [1993]; Lau [2003]; Redlawsk and Lau [2013]). At the very least, decision strategies involve plans for gathering relevant information (from the external environment, and/or by search through memory), evaluating that information, and choosing among alternative courses of action.
Lau and Redlawsk described four broad types (or, in their words “models”) of decision strategies that are employed by citizens in making vote decisions. These four strategies differ in how much information is gathered (depth of search), and how evenly that search is distributed across alternatives (comparability of search)—the two major dimensions identified by psychologists across which various decision strategies differ (e.g., Jacoby et al. 1987; Ford et al. 1989; Payne, Bettman, and Johnson 1993).
...
We also propose a fifth possible type of decision-making, one that gets more attention in the popular press than among psychologists, and is colloquially referred to as “going with your gut.” Keeping this common colloquial label, strategy 5, Gut decision-making, is strictly affective, usually unconscious, and involves no deliberate external searching for information. It should surely be associated with shallow information search, with no effort whatsoever to compare alternatives on anything other than how they make you “feel” (Dane, Rockmann, and Pratt 2012). Allegedly, it often provides very good decisions—or at least choices that, retrospectively, decision-makers feel good about.".
As you can see, the quality of each vote (up / down, even abstain) can vary greatly.
