As for the popular vote in the US, this indeed does not diverge too far from 50-50 (although note that at state and especially at county level you will easily find extremes, and they are getting more and more typical).  For referenda, I don't know whether empirical evidence supports the observation that tight 50-50% result occur more often than just by chance, but let's assume for now that they do.

What is explaining it? Well, there are probably different situations and explanatory factors.  But I am thinking now of the following hypotheses which may at least explain parts of the phenomena.

1. For the US popular vote: it is typical, not only in the US, that the population will grow fatigued with the party giving the president after a while. People who could be convinced by enthusiastic activists to vote for the now-president will not turn up again to vote for him(her). Maybe even your local activists will lose their faith and put in less effort.

- Also, the supporters would probably have benefitted from new policies that the president brought but they are satisfied now and don't see much to gain. The opposition can promise more ('Change') and their policy offering starts to seem more appealing, and more important for certain groups not favoured by the current adminisitration.

So if you won the presidency, chances are that after your second term the other party will win it. But they wouldn't have enough time to accumulate a huge lead before actually winning, as voter shifts in established democracies are usually slow.

(I am sure there is good literature on this already, would be interested to hear about it)

2. For referanda: a new cause, when it is first formulated only has little population support. It needs to gain enough popularity to have a chance of winning a referendum. But if it gets to a level of popularity where it is obvious that this is what voters want, politics will want it implement it anyways, without a referendum.

Only if it is a real question what the population wants, does it make sense to hold a referendum.

Dear Mate Peter

Regarding your first hypothesis, there seems to be some support from post-WWII elections:

From a quick check on the data since 1824 in the ref linked below (copied and sorted into Excel spreadsheet, also attached), it appears that while in recent elections, two-term presidents have often been followed by a change of party, (5 times since 1960 and only once prior), in early elections it was the converse, 7 times down to 1944, and only once since then (if you add in the unquantified data from the Timeline figure in the Wikipedia article, the elections prior to 1824 increase the no-change count further).

That’s a distinct change, from disagreeing to agreeing with your 1st hypothesis, between the pre- and post-WWII eras.  

My guess as to a possible reason for this shift is that communication was much poorer in the earlier period and may have played a role - "Better the devil you know..."

If you examine the Timeline diagram in the Wikipedia article, it also shows that votes were:

·         Fairly close to 50/50 for much of the 2nd half of the C19th, and also since 2000

·         Fairly disparate in the early C19th, and most of the C20th.

But I don't see anything in the national franchise changes (3rd item below) that would easily explain this.

Regards - Paul

https://en.wikipedia.org/wiki/List_of_United_States_presidential_elections_by_popular_vote_margin

https://en.wikipedia.org/wiki/Voting_rights_in_the_United_States