So, this card has received a lot of hate in my local meta. Words like 'it is just objectively bad', 'strictly worse than putting in better cards', and 'the math doesn't work out' have been rather liberally bandied about. Which made me think a fair amount about evidence against such statements. I'm happy to see that most of what I wanted to say has already been said. Great job Netrunner community! Nonetheless, I'm going to try and convince you that not only is this card not objectively bad, but it's actually fantastic in the right build.
The criticism I want to attack most directly is that the math doesn't work out. In my mind, when discussing economy most Netrunner math starts with a fundamental ratio
1 card: 1 :1
Building economy for your deck is all about how you warp this ratio in your favour. Magnum Opus doubles your click efficiency giving you 2 per while Professional Contacts does so by giving you a card and a for each click. But of course, they don't offer you this efficiency for free. You need to invest and in that case of Magnum Opus, as well. These are great examples because it's fairly obvious how their efficiency works. Okay? Cool.
But we're not talking Shaper here, we're talking Criminal And to be clear, this really is a Criminal card. As tiediedvortex points out, you want to run all 6 and I can't imagine any deck sparing 6 influence for it. Also, this is a draw engine with economy attached and not the other way around. So let's compare it to some event based draw in criminal. It's a pretty short list. Fisk Investment Seminar. And done. Oh, did we mention it was priority and gives your opponent that same amount of cards? Economically it nets you only 2 cards (over what you were already getting anyway) and it still sees play. So Exclusive Party is either the best or second best event draw Criminals have. Sure, there's also Drug Dealer but again it comes with the drawback of negative drip economy you can't turn off and it's a resource.
What about in faction event based economy cards? What if we put those in and and just to draw? I think the most fair comparison would be to ditch your 6 Exclusive Party and add 3 Sure Gamble and 3 Easy Mark. If I play all of those, I net 21 (3 for each Easy Mark and 4 for each Sure Gamble)...but I'm also down 6 cards. So really by our fundamental ratio I net 21-6 = 15 if I want to replace those cards. That's an average of 2.5 per click I spent playing those cards. Which, what do you know, is exactly what you're making on Exclusive Party if you play them all. Of course, when you get that money is very different. We can't know what order you'll draw your EM and SG so let's assume that you are making the 2.5 average each time. The tipping point then is at card 4. At that point you've made 14 on average and are down 4 cards, net 10. Exclusive Party has made 6 and 4 cards, net 10. And let's not forget the potential tempo hit that comes with Sure Gamble - you have to click up to 5 if you want to use it sometimes. Exclusive Party is never a tempo hit, you can always play it immediately for effect if you like. So I will disagree with tiediedvortex here. You should expect to see at least 4 every game to be as good as the alternative event economy, although there is no doubt you want 5 and 6 (again presuming you don't trash any without playing them, I'll happily discard one of these on an opening Andromeda: Dispossessed Ristie hand)
So, the math works out when you build a deck where draw is more important than burst economy. The most obvious case is combo decks, like stealth that sees lots of play in criminal or Snitch & Au Revoir. You need to get your pieces out fast. Let's not forget you can go tag-me with this economy without fear.
So far we've just talked Criminal card pool. Street Peddler would work well with it or Faust as Yziel mentioned. It could even possibly work with Faust and Drug Dealer combos which giving you burst money when you need it. I think this is a subtle and well-designed card. It's not as obviously 'good' for all decks as something like Sure Gamble but it plays an interesting role for Criminal builds. Sorry I'm so long-winded.