In the USA it's not even tyranny of the majority. The Republican candidate secured the presidency in 2000 and 2016 while receiving fewer votes than the Democrat, and in 2000 probably only did so because of lobbying and legal pressure on a Supreme Court where a majority were appointed by Republicans (and I'll remind you again the winner's brother was the governor of the state in question). The Senate has two members per state so is inherently biased to smaller and more rural and therefore more Republican states, and many districts in the House and in state assemblies are "gerrymandered" because the party in power gets to set the boundaries. Apparently also if the electoral college is tied the House gets to choose the President, but rather than having a straight vote the votes are one per state (cast for the party with more representatives from that state) so the same bias applies as in the Senate.
So in multiple ways the system appears to be rigged in favour of the Republicans. I've gathered this from mainly progressive news sites but they appear to be reporting fact so I don't believe the filter bubble effect applies - if anyone disagrees with me then please politely point it out...
Maybe not
deliberately rigged in favour of the Republicans, but certainly biased in a way that happens to benefit the Republicans at the moment (though future electoral shifts could change that). You are correct that the disproportionate representation given to smaller states in the Senate is unfair, and it happens at the moment that those states tend to be Republican. It's also worth noting that neither Puerto Rico nor Washington DC gets federal representatives - and both are strongly Democrat. On the other hand, gerrymandering the constituencies is I think done as much by Democrats as Republicans - indeed, it was a Republican - Arnold Schwarzenegger - who as Governor of California tried to put a stop to gerrymandering at least in that state, but was defeated in a referendum on it.
Trump's victory in 2016 despite Clinton getting more votes was arguably as much down to his securing
very narrow victories in some large Midwest states and in Florida - and with the winner-takes-all system, that meant him getting
all the electoral college votes for those states despite having barely 50% of the vote. Meanwhile, in states like California, the Democrats were uselessly piling up absolutely massive majorities in the popular vote when a majority of 1 in those states would secure them just as many electoral college delegates. First-Past-the-Post really benefits parties who can distribute their votes so as to secure very narrow pluralities in their areas.
On the other hand - a possible hope for the future: Texas - once solid Republican, and with a massive number of electoral college votes - is moving inexorably in the Democrat direction thanks in part to demographic changes. If that trend continues - and there's currently no reason to doubt that it will - then at some point, probably in the next 10 years or so, Texas will start narrowly voting Democrat. And when that happens, the Republicans could suddenly find that the electoral college makes it harder, not easier, for them to elect presidents.
One thing where you could argue that the system is slightly and deliberately rigged in favour of the Republicans is where Republicans have repeatedly and often successfully sought to make it harder for poorer people or ethnic minorities to vote, effectively disenfranchising some people who are more likely to vote Democrat.