Well, the double jump raise to game in a major surely doesn't represent today the hand your mother used to hold. Many can remember when that bid showed responder had an opening hand, but with sometimes as few as three card support. Marty Bergen and Larry Cohen changed all of that with their explanation of the Law of Total Tricks and the implementation of Bergen Raises. While the "Law" has been under some attack lately by Mike Lawrence, experience has shown that it is still a good guideline and that on distributional hand it works more often than not. In the context of the double jump raise, the "Law" would say that if partner and I have 10 trumps between us, we need to compete to the 4 level. Thus, today the bid most often shows a hand with 5 card trump support.
I have been moved to do this post by three recent experiences. First, two weeks ago I had this sequence with a new partner. His hand came down with xxxxx, xxx, Q, AKxx. the hand fit like a glove and we made 6 spades with my 14 hcp hand which was AKxxx, x, AKxxx, xx. Although partner was neither right or wrong in his bid, it did show the need for us to adopt a standard for this bid. I did not expect that he would have the hand he put down (the operative word is "expect"). After the session we talked out the sequence and reached agreement that his hand bid was really too strong for this bid with the 2 quick tricks outside the trump suit and the single queen of diamonds. In our little partnership we agreed the bid would show 5 trump and not more than 1 quick trick outside the trump suit. In essence, we agreed to go with the Law of Total Tricks and take up opponents bidding space with poor hands with a wealth of trump.
The next week with the same partner we had the same sequence. Again I had a very good one spade opener (4 losing trick count) that needed only a couple of key cards outside of trump to have a real play for 6. I went into the tank wondering if partner really remembered our discussion of last week. It finally came down to the fact that I had to trust my partner and not try to outguess him. I passed this nice hand and partner put down Jxxxx, x, xxxx, Qxx. I could not help exclaiming "excellent partner." Even with this cow dung we easily made our game and 6 spades was never close.
When I picked up the February Bridge Bulletin, in Eric Kokish's column "Our reader's Ask", the first question was about a jump raise to game on JTxxx, xxx, xxx Jx. The vulnerability was unfavorable and the game was at IMPs. Opener had slightly better than a Rule of 22 opening hand (11 points, 9 cards in two suits and in his case 3 quick tricks), and in final result the hand went for -1100. Although Eric ultimately said that responder's bid was one that he could not support under the given circumstances, he was careful to point out that it all boils down to the partnership's understandings and expectations.
If you and partner agree to strictly follow the Law of Total Tricks in your double jump raises with weak hands at all vulnerabilities, then the 4 spade response is correct and within expectations. The bidding in that case is correct and only the result is wrong. That should not cause recrimination at the table, but may cause you to re-examine the partnership's standards. Even as a strong "Law" advocate, I don't want to bid 4 spades ("red vs. white") with that hand, and particularly at IMPs where I might be sent to the partnership desk by my team. I am not going to pass on that hand, but I see nothing wrong with a weak jump raise to 3 spades to add a measure of safety. Yes, you have one more spade that you haven't told partner about, but as Eric Kokish points out in his comment, "there is only so much 'law' protection you can get from the 9th and tenth trumps."
Now that we know what to do with the hand that qualifies for the double jump raise, what do we do with the awkward hands that have 5 trump, and have that AK outside, but not Jacoby 2 NT values? We bid 1NT forcing, and at our next turn we bid 4 spades. Now partner will be able to perfectly picture our hand and act accordingly. If you don't play 1 NT forcing, simply make any temporizing forcing response, and then bid 4 spades at the next opportunity. This is not as neat and shows the facility of the 1NT forcing bid.
The thrust of my post is not what I would bid with the hand or what Eric Kokish would do. It all boils down to you and partner developing a set of expectations for the jump raise response so that opener will know what to do with his hand. If one time responder has the hand I first described and the next time has the hand that I described second, opener, as the captain of the ship, is literally going to be "lost at sea".
The concept of having partnership understandings and expectations is much broader than the example that I discussed. As Eric Kokish states, most everyday bridge disasters are not the fault of the lack of experience or the lack of ability, but rather the lack of good understandings with partner.