索性 is similar to 干脆 or 就, that is depending on how you understand these two words in use. In the dictionary 索性 is given a definition of "might as well" or "simply", while in my notes I have "without hesitation" written. My dictionary uses two examples with 既然, which obviously complicates the understanding of this word.
既然已经做了，索性就把他做完。 - Since we've already done it, we might as well finish it. (What kind of fucking dictionary is this anyway? I mean, seriously, what does that fucking chinese sentence mean?) The translation in the dictionary is just incredible (Since we've already started it, we better finish it.)
Since 既然 means "since" in the sense of a "compromise", the second clause necessarily will always read "might as well" if it makes sense that way. Example:
既然你已经做了，就把它做完（吧）。 Since you've already done it, you might as well finish it.
To me, 索性 really can be used in exactly the same way one would use 就 with an optional 吧 at the end of the sentence.
On the internets it seems some collocations utilize 索性 like 索性放弃 but, imagine in actual use one can almost always use 就。 Given that, if one must absolutely express the concept "might as well" which every dictionary insists is 索性's 定义 without a 既然 introduction, and 就 cannot replace it, you have to use 索性。 For example, from the internet 索性做了和尚， 索性再醉一回。
The problem is everywhere everyone insists 索性的近义词是干脆, but I can nowhere find 干脆 with that kind of usage/meaning. I really don't think 干脆 means "might as well" while I do think 索性 likely means that. The 相同点 is merely the directness/bluntness the “simply" or "just" or as the they say the "straightforwardness" of the two and their swappability in some situations. I really don't think 干脆 means "might as well", but people translate it into "might as well". On the other hand, its entirely possible 干脆 has picked up this meaning or in chinese this discussion is entirely irrelevant because this level of distinction entirely doesn't exist (very likely).
If you go on nciku you can see a little comment about this issue which is not so curiously left out of all teaching materials and dictionaries (not unexpected at at all), but as usual their write up is pretty useless.