It comes as no surprise to me that the option "yes, but only in appropriate situations" is the second most popular on this poll. After all, "appropriate" is a word that might apply to any given circumstances within a person's ideals, so naturally the option has wider appeal than the others. In a controlled poll to really find out the answers on this, you'd want to change the language a bit to narrow things down and specify exactly which "situations" are implied by the answer.
With that said, it is an answer that I agree with within my ideals. You see, being topless is allowed for men, and therefore it should be allowed for women, since otherwise there is inequality between the genders. While it has to be noted in a pragmatic manner that human nature, or at least men's nature, is to enjoy the sight of breasts, this is actually true whether there are clothes are not. In fact, in some African cultures, where topless women are common, it is actually considered more arousing for women to be wearing clothes, so that portion of attraction is mostly environmentally inspired, with the theme of forbidden fruit repeated in every culture, wherever the fruit tree may be planted (usually away from what is normal or common).
If it is true that whatever is not normal is what is sexy, then it is very likely that allowing women to be topless in public places will only have a short term negative effect on the actions of men who find this attractive, since after a generation of this being the law, clothes will suddenly appear more attractive again. Unless great value is placed on the short term outcome over the long term benefits, it makes sense to allow women to go topless wherever it is appropriate.
However, like I said earlier, "appropriateness" is a concept that varies depending on your world view. While it might be appropriate to us for a woman to go topless in a swimming pool or at the beach in Australia, Britain or (some of) America, it may not be so acceptable, say, in Iran. In the Western world, the change of rules would be correct both socially and idealistically, but would run against difficult opposition from religious groups and migrants from places where it is not considered to be acceptable. This means that the rule will probably take a long while to become law anywhere notable - cultural erosion of old values will most likely result in it nonetheless later on. Not to mention, the controversies about where it would be appropriate to go topless could divide people enough to stall any change further. Hopefully a blanket ruling in favour of it will be the first result, followed by amendments where this becomes a mistake. That is probably the best way to go about this legislatively.
There is a chance that there will be a breakthrough with this soon, as the older generation is switching to the baby boomers, who were young during the Cultural Revolution and the expansion of feminism under the leadership of people like Virginia Woolf. Of course, some of these people have become more conservative with age, but the Cultural Revolution is still continuing in many ways today, so liberalism will probably increase in power.
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