There are two different pronunciations recorded for the "th" sound in the English word "with" in most dictionaries (Webster, OED). I was wondering if one or the other is preferred in certain phonological contexts (e.g. voiced "th" as in "that" before voiced consonants or vowels).
I generally produce ð in all contexts (even pre-pausal), but I have heard people uttering pre-pausal θ. You could approach the question from an individual phonological perspective, but once you start talking about probabilities, you're really in the realm of socio-phonetics. I don't see any reason to assume that all English speakers have the same representation of the word. As far as I know, there is no general phonological tendency to assimilate voicing of final /θ/ or /ð/ to what follows in dialects of English, though there are always problems detecting vocal fold vibration in fricatives in speech. If there is contextual variation for some speakers, it is more along the lines of phrasal allomorphy of the type "a ~ an" or "ði ~ ðə".