There are many different approaches. First of all, it depends who you’re trying to poll. Some polls are about very particular groups of people, which might make things far easier or harder. For example, if a company wants to poll its workers, it can reach them with its internal email system and chase up anyone who doesn’t respond. On the other hand, if you want to conduct a poll of, say, drug dealers, you will have a very hard time sampling the relevant population or even estimating how large it is.
Political polls are usually aimed at broad swathes of the population, typically “registered voters”, “likely voters”, or “all adults”, so the above factors don’t apply. Depending on where in the world you are, it may be possible to access a reasonably complete list of residents with contact details, or you might have to resort to methods such as dialling phone numbers at random or advertising online. However you do it, a significant fraction of the people you contact will not respond, and these people will be skewed towards certain demographics (e.g. they might have a tendency to be younger or older than average). Pollsters typically deal with this by limiting the number of people from demographics who are overrepresented, or by weighting their responses (e.g. if there are twice as many men as women, you might count each woman’s response twice). The problem is that there are numerous different ways you could divide a population into demographic groups. You need to try and focus on the factors that most affect people’s opinions (e.g. it’s important to get a 50:50 gender ratio if men and women tend to have very different opinions on the issue you’re asking about). This ends up being more art than science.
Another important factor is the question wording. It turns out that people are often quite strongly influenced by subtle changes in the wording, e.g. “Do you agree that…?” tends to get more “yes” responses than “Do you think that…?” This is because there will usually be many people who are on the fence or who haven’t really thought about the matter at hand, so it doesn’t take much to tip them one way or the other. Again, this is more art than science.
And it should be pointed out that pollsters are not necessarily trying to avoid bias. Ultimately they’re working on behalf of their owners/clients. If a client is willing to pay a lot of money to ask a slightly biased question to try and skew public debate, most pollsters will not turn them down. Some particularly unreputable pollsters have been known to fabricate results, or conduct “push polls” in which they contact very large numbers of people, ask them biased questions designed to change their opinions, and don’t even record the responses.
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