Without an educated citizenry, democratic rule is bound to fail. Democratic rule means that the people select their leaders and give them informed consent to rule with authority. Unless the citizenry is educated, informed consent is often impossible. Not only does the population need to be educated in order to give informed consent, but without education the people can be too easily led by the wrong kinds of leaders, leading to possibly more costly mistakes or worse.
At many levels and on certain issues, the electorate in a democracy will vote directly upon a proposal, especially at the local levels. What this means is that the electorate must understand the issues at hand completely and the consequences of any decisions. Many issues are extremely complicated, even though they look simple. One example might be a proposal to raise property taxes on large developments and downtown buildings in order to fund construction of a new recreation center.
Without education most people cannot know all the economic implications of something like this. They may think it is simply a matter of taxing big business in order to get something for the whole town, when, in reality, the higher tax will result in lower needed investment in the town, and the resulting higher cost will be passed on to the consumers, thus adding to inflation and raising the cost of the proposed recreation center. This is just one small example of issues that are often decided by the populace in a democracy. In addition, without education, people will not be literate, and so will not be able to research anything.
In addition to having to vote directly on complicated issues, the electorate in a democracy must choose its representative government officials who will make many more very important decisions. Again, literacy is required for them to know what they are deciding. Also, without education, many people will choose based upon emotional reactions, and unscrupulous politicians will use emotional triggers to get votes.
Any politician who does this is not likely to care much about really representing the best interests of the people, since they do not mind using deception to get votes. Democratic rule allows us to select our best leaders, but if the populace is not educated then the leaders will not be of the people, but of a separate elite class, making is very difficult for even the best intentioned to even know what the people want or need. Education provides the tools to become informed upon any subject and make well reasoned decisions, including choosing among candidates for public office based upon something more solid than emotional cues. It also helps people to understand what the politician is really saying in a given speech, which often is very little. A good education will encourage people to stay well informed and participate in their government.
So if the populace is not educated, poor decisions on issues subject to direct vote are much more likely. Worse, it becomes very likely that they will elect someone by popularity and not substance. At best, it can result in the election of lazy egocentrics who simply want an easy job, and at worst it can result in a total change of government in smaller democracies or costly mistakes, because the elected official is not equipped for the job. At worst, smaller democracies will collapse completely, promoting take-over by another form of government, possibly totalitarian, and larger ones will find themselves in a recession and looking bad to the rest of the world. Therefore, an educated populace is necessary for the survival of a democracy.