Not really an experiment because of the lack of control, but I do have some numbers.
My broker dwarf started with 5 Negotiation and 1 Judge of Intent, and also 2 Consoler / Pacifier for dealing with unhappy dwarves. He made five trades before wandering off for something to eat despite being burrowed in the depot, so a miner ended up taking over and doing two more trades. Experience points were totalled as the traders left, which may have allowed the original broker some time to stand around in the meeting area.
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Broker social stats, before and after:
Appraiser: 0 to 3737, 3737 gain
Negotiator: 3651 to 3737, 86 gain
Judge of Intent: 646 to 720, 74 gain
Persuader: 144 to 231, 87 gain
Intimidator: 153 to 242, 89 gain
Comedian: 169 to 251, 82 gain
Flatterer and Liar: 0 to 0
Consoler: 1242 to 1248, 6 gain
Pacifier: 1250 to 1256, 6 gain
Conversationalist: 155 to 160, 6 gain
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I originally counted Pacifier because I thought it might be useful for calming down irritated traders, and Conversationalist because I believed it to be one of the trading skills. Consoler was just there, not sure why. The gains in those three skills compared to the other skills suggest that they were gained in post-trading chat and not during trading, as XP gain seems to be pretty even across used skills. Also I was counting gains by percentage because I don't think DT has a persistent screen showing XP for individual skills, and at Dabbling level a 6-point gain should be enough to add 1% to the progress bar.
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Miner social stats, before and after first trade
Appraiser: 0 to 0 (Appraisal skill is only ever gained the first time the trade window for a particular caravan is opened)
Negotiator: 272 to 284, 12 gain
Judge of Intent: 232 to 240, 8 gain
Persuader: 280 to 286, 6 gain
Intimidator: 254 to 263, 9 gain
Comedian: 286 to 294, 8 gain
Flatterer: 249 to 256, 7 gain
Conversationalist: 276 to 276, 0 gain
Liar: 0 to 0
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The first trade was fully successful and got me everything I really needed. The second consisted of a few unsuccessful trades, and then one successful one after I increased the profit. Since the trader was ecstatic to begin with I could afford to be cheap for a bit.
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Miner social skills, before and after second trade
Appraiser: 0 to 0
Negotiator: 284 to 314, 30 gain
Judge of Intent: 240 to 271, 31 gain
Persuader: 286 to 322, 36 gain
Intimidator: 263 to 297, 34 gain
Comedian: 294 to 327, 33 gain
Flatterer: 256 to 292, 36 gain
Conversationalist: 276 to 276, 0 gain
Liar: 0 to 0
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So it seems as though any relevant skill is raised by a trading attempt, successful or not. It also seems as though comedy is more important than conversation when brokering deals. Appraisal on embark is not necessary for informed trading as the skill will be gained quickly before any trading is done, but will be required if you want to know item and fortress worth before that point. Your broker also needs to be the one in the depot when the trading screen is first opened, otherwise the XP will go to a non-broker dwarf and you'll have to make that dwarf the broker to start seeing item and fortress worth.