A colon usually implies one of two things:
- What follows the colon is a list or enumeration of things (as with the colon preceding this list)
- What follows the colon is some kind of explanation or expounding on the sentence that comes before it
In your sentence, neither is really the case. “In this case, the rights of the neighbor to the security of his property” is very obviously not a list, but it’s not really an explanation or a more detailed expounding on the first sentence.
The semicolon has a wide variety of quite complex uses; but the most common one is when you need something a bit stronger than a comma, but not quite as separative as a full stop. In your sentence, a semicolon is arguably appropriate.
To me, however, the fragment at the end of your sentence is more like an added afterthought to the main clause—a sort of side remark narrows down the meaning of “rights of individuals”. As such, I’d say the most appropriate punctuation mark would be exactly what I have used for a similar side remark in this paragraph: a dash.
Strict liability serves to uphold the rights of individuals—in this case, the rights of the neighbor to the security of his property.