First Keegan Bradley at the USPGA Championship last August, then Webb Simpson at the US Open last month, now an Open one-two of Ernie Els and Adam Scott at Royal Lytham.
The link? They have all used long putters - although the list may not get much longer.
"This decision has not been taken, but I think we are going to say something in a few months rather than years," Dawson said.
"There are further discussions to be had, but if the rule is changed it would come into effect on January 1 2016."
The Rules of Golf are reviewed on a four-year cycle and that is when the new rulebook will be published.
"I'm not sure if it's true, but this may be the first one (major) where we have had the winner and runner-up with long putters," Dawson added.
"Let me say that the Open Championship result does not have a direct bearing on the discussions about long and belly putters. They were going on well before what has happened.
"The situation is that the R&A and the USGA do have this subject firmly back on the radar.
"We appreciate that there is much speculation about this and that we need to clarify the position as soon as possible.
"The initial determination has been that we are examining the subject from a method of stroke standpoint rather than length of putter standpoint."
Asked for data on how many players now use long putters he said: "We do monitor it and I think the biggest event last year was something like 21%, but it seems to be averaging about 14-15%."
In The Open last week, however, there were 27 long putters and 16 belly putters in the field of 156. That works out at 27.5%.
"It hasn't yet backed its way all the way down the game, although the statistics would show - and I've checked this with the manufacturers - that at the club level or recreational level they are much more used in the United States than they are anywhere else in the world.
"The objections I find from those who object at professional level, at elite level, are all about 'If people have become failed putters in the conventional way, why should they have a crutch to come back and compete against me when I haven't failed in the conventional way'.
"That's the general argument one hears, but we're also seeing now people who can putt perfectly well in the conventional way thinking that an anchored stroke gives them an advantage.
"I think that's the fundamental change that we've witnessed in the last couple of years.
"Anchoring is what we're looking at, method of stroke, and it's all about putting around a fixed pivot point, whether that fixed pivot point is in your belly or under your chin or on your chest. I don't distinguish.
"It doesn't detract in any way from the winner as long as he obeys the rules of play at the time. Bobby Jones used concave-faced clubs for some of his major championships and hey were outlawed later.
"Bobby Jones's victories are in no way demeaned as a result of that and I see that in exactly the same way."
Even Els has come out against long putters in the past, but he also famously commented: "As long as it's legal, I'll keep cheating with the rest of them."
Tiger Woods has stated: "I've never been a fan of it. I believe it's the art of controlling the body and club and swinging the pendulum motion.
"I believe that's how it should be played. I'm a traditionalist when it comes to that."