The short answer is 'Yes' - but of course, it's a little more complicated than that.
Each Civ has a level of Cultural Influence on other Civs in the game. The level of Cultural Influence is based on their cumulative Tourism since they met the other Civ as a percentage of the other Civ's cumulative Culture from the beginning of the game.
Here are the possible levels of Influence based on that percentage:
- Unknown - <10%
- Exotic =>10% but <30%
- Familiar =>30% but <60%
- Popular =>60% but <100%
- Influential =>100% but <200%
- Dominant = 200% (the game stops counting at this point)
Ideological pressure is calculated by the difference between your level of Influence on a Civ and their level of Influence over you. For each difference in level, the Civ being influenced will receive one point of Ideological pressure.
So if you are Freedom and you have Exotic Influence with an Order Civ but they have Popular Influence with you, they will inflict 2 points of Ideological pressure on you.
This same calculation is made for every Civ in the game and then all Ideological pressure points are calculated for each different Ideology. The Ideology that supplies the most pressure points will be the one that your people will favour (and will switch to if you are forced into a revolution). I'm not absolutely sure what happens in the event of a tie but I
believe from my observations that the Ideology which has been around for the longest will win out or that the Ideology of the Civs with the highest Tourism pressure will win out.
So taking all this into account, if you have very poor Tourism/Culture but a lot of other Civs who have
high Tourism switch to your Ideology, their pressure will offset the pressure from any Civs that have opposing Ideologies. If the balance tips in favour of your Ideology, your people will settle down and become 'Content' and you will stop losing happiness.
All of the above can be augmented by having your Ideology voted in as the World Ideology. Doing this will immediately add 2 points of pressure for your Ideology to
all Civs on the map, regardless of Influence levels.
Check the Culture panel and go to the 'Culture Victory' tab for more details. If you mouse over a Civs ideological status ('Content'/'Dissidents' etc) you will get a pop-up which breaks down the Ideological pressure that the Civ is getting and it will sum this up by saying which Ideology that Civ's people prefer.
Sorry for the long read - hope it makes sense!
PS: In case anybody is interested, the unhappiness that is inflicted is based on the number of cities
or the amount of population that you have. For each point of Ideological pressure inflicted on you, you will get 2 points of unhappiness for each city that you have
or 1 point of unhappiness for every 10 points of population that you have. Whichever total is higher. So generally, the bigger you are the worse the unhappiness hit will be (standard size map/speed).