"The Wisdom of Crowds" is a book (1985) by James Surowiecki describing how a crowd can be wiser than an expert. The crowd collectively has more information and if this information is properly aggregated, it will make a superior decision. Such ideas have roots in Condorcet's Jury Theorem (1785), which states that with enough unbiased jurors the correct verdict will be made.
While these are supportive that democracy can work, there is a problem of using elections to aggregate information and make the best decision for society. This problem is that every vote counts equally. While this might seem fair, it does not always lead to the best choices. People that care less about issues count just as much as people that care a lot about the issues. Likewise, those that are less informed count the same as those who are more informed. We can see this with the following example.
If three friends are scheduling a dinner and two dates are available: Monday and Tuesday, it is not advisable to take a vote since two may mildly prefer Monday, while the other may have to miss something important to make it on Monday. If the friends are choosing which restaurant to eat at, again, a strict vote would not always work the best since perhaps only one of them tried a particular restaurant. Communication among friends solves this, but with larger groups that are not able to communicate or willing to listen to each other this will not work.
One seemingly radical solution is to not make every vote count the same. Those of potentially better informed parties would count more than those of worse informed parties (or those that are most affected by the outcome count more). For certain decisions, such as those made by companies, this is feasible. In "Identifying Expertise to Extract the Wisdom of the Crowds," winner of the 2016 Exeter Prize, Budescu and Chen use past performance to find experts in a crowd and count their views more. The company Goodjudgment (where Chen is now employed) is working on commercially implementing such a solution.
In "Vote or Shout," myself and Chakravarty consider replacing voting with a "shouting match" where the noisiest person gets to decide. This can be thought of a system with lobbyists. Since shouting is costly, the better informed or the one that cares the most will be more willing to shout the loudest. This will be beneficial in the case of a new restaurant where it is likely that at most one of the friends have tried it or in the case where the days are, for the most part, equally available to all and only occasionally there will be a conflict.
Despite other options, we still may wish to stick to one equal vote per person. However, we can take advantage of the lessons learned from above. In "the Benefits of Costly Voting," myself and Chakravarty and Myles, we find that a wasteful cost to voting such as making it difficult to register, particularly at the last minute, or less convenient to actually vote, can improve outcomes by filtering out the voters that care less or are poorly informed.
This research sheds light on what can go wrong with polls. Those willing to answer polls truthfully are those that feel more strongly about the issues and that gathered information. The 2016 presidential election and the Brexit referendum also had another two compounding effects: First, voting for one side (Trump and Brexit) involved a certain amount of shame. One needed to feel quite strongly to say that they are voting for that side. In certain areas, friendships and business relationships were threatened if one did not support the "correct" side. Second, the knee jerk reaction for someone deciding upon the spot was to vote for Trump/Brexit -- anti-establishment. This combination caused the polls to be inaccurate.
What can we do to improve elections in the future? For one, the practice of shaming or demonizing someone who doesn't agree with one's position is not the way a well functioning democracy should work. This hurts information aggregation. A CEO or political leader should not fill senior posts with yes men. In addition, one must take care when voting is made easier (and avoid making voting mandatory). The UK Labour party substantially reduced the barriers to voting in 2015 and perhaps did not get their best possible leader. Keeping at least some reasonable cost will stop those with less at stake and poorly informed from voting, leading to better outcomes overall.