They will be content to do so because they are satisfied that they have a better chance of getting their views accepted and passed into law by operating as part of their party rather than as a single individual - and they will calculate that, since they can enthusiastically support the bulk of their party's programme, it is on balance worth doing, even if it means forgoing their own position on a particular issue.
There will be very few parliamentarians, however, who have never struggled with the conflict between what they think as an individual and what is the decided policy of their party. Most MPs, and this is certainly true in my own case, will have, at some point or another, found it necessary to "defy the whip" on an issue on which their view differs from that of their party and is one on which they feel strongly or that involves what is, for them, a matter of principle.
The party whips will, in most such cases, be forgiving of such lapses in party discipline and, in truth, the cohesion and continued functioning of the party system would be at risk if discipline were imposed too severely.
Indeed, it could be argued that the system as a whole depends on the occasional willingness of individual MPs to break ranks and stay true to what they believe, irrespective of what their party demands of them.
We can see such a situation unfolding before our eyes as the impeachment of Donald Trump proceeds. The American system is not a parliamentary one, but in the case of an impeachment trial, senators - like MPs - have to choose whether to cast their votes in accordance with the requirements of their party or whether to follow their own individual consciences.
The signs are that the President will be able to avoid removal from office because his fellow members and supporters of the Republican Party will hold their noses, grit their teeth and close their eyes, and serve the interests (as they see them) of their party rather than of the country as a whole.
The evidence for the President's unfitness for office surely becomes more overwhelming by the day. Those of us who are citizens of the world and who are privileged to live in a democratic country are, one would hope, entitled to expect that Republican senators will recognise not only their responsibilities to their own country but also to world peace, and will place them ahead of any duty they owe to their political party. Sadly, it seems likely that they will get their priorities wrong.