I suggest that new posts (questions and answers) should start at +3 votes by default rather than at 0.
This is meant to have no mechanical effect on the website. It is just a psychological display trick, with two effects:
Askers who have a question downvoted will not think Wow, my question is so bad that it has negative value for this site, and will be less discouraged. This is merely a psychological trick, but hey, haven't we all inconsciously been tricked sometimes, for instance by a price set as $9.99? I have had experience that, for instance, when setting the mark scale for an exam, it feels better for a student if their vote does not go into the negative; this can be achieved for instance setting values such as 1 point for a missing answer and 0 for a wrong one rather than 0 and -1.
On SE, people sometimes feel the need to delete questions outright if they get a couple of downvotes, which is not a good thing: maybe they can be salvaged, or they only contain a minor mistake by a new user. Or maybe that downvote comes from a grumpy user that randomly happened to be the first to see the post, and it will soon be cancelled by several upvotes.
Voters will think twice when they downvote a question from 1 to 0, or from 0 to -1: is this question really that bad? Aren't those 2/3 downvotes enough to send a message that this question is not OK? A question should be downvoted more than 2-3 times only if it is egregiously bad. On several SE sites long-time users exercise some restraint with downvotes already, but this trick would make it more natural.
Another argument is that starting at 0 is not necessarily the correct thing: one could argue that there is at least one person who finds the question/answer useful, the poster, so it should start at 1. I believe Reddit posts start at 1, for instance.
Note that SE already does something very similar with reputation (and for exactly the same reason).