How to get someone to take responsibility

We don't choose how tall we are, the colour of our eyes or any other physical attribute. This is obvious, and we don't take responsibility for these qualities - they are a given, biologically determined. If you were to apologize for your height and promised to change it no-one would believe you'd be successful at that task and would never expect you to try.
Less obvious is the biologically determined parts of our character. We don't choose to be heterosexual, or any other permutation of sexual preference. If we don't choose what we are attracted to, or the potency of that attraction, we also don't choose the dilation of our eyes or the increase in heart rate when the object of desire comes into view.
If we don't choose the way our mind and body are affected by a stimulus such as desire, it is also true that we don't choose our response to things that make us afraid. Or happy. Or depressed. And so on. We have an intuition that we are choosing our responses to the world moment-to-moment. If this isn't true, then how could anyone "take responsibility" for their actions?
Our environment produces changes in us. When it is hot we perspire, when it is cold we shiver. We can sweat without knowing we are sweating, or we may notice the perspiration. If we notice our habitual response to temperature, then when someone asks if we will respond to temperature changes, then our answer will be "yes". Now we are able to inform others of our probable response to an external stimulus. This is level #1 of responsibility-taking.
If cold temperatures habitually produce associated responses related to the physical response of shivering - flexing forward, holding ourselves with our arms and mentally as well as physically contracting, for instance - then those responses are also not "chosen" by us, as we couldn't choose to respond to cold much differently. Emotional responses associated with the cascade of physical responses related to temperature changes are also then not "chosen". If deep cold causes you to feel great discomfort, then waiting in the cold for a friend to arrive who is late may amplify the frustration you feel toward them. You would naturally associate their lateness as a contributor to your suffering. If it were instead a gorgeous spring morning, your impatience would decrease substantially.
So, outward environmental changes can affect our emotions, producing responses to those changes. But we also have an inward mental environment. We have the language we learned as children that we form concepts with. We have a baseline, biologically determined level of concern about survival that's been handed down for millions of years by our ancestors who survived to reproduce. There are many more aspects of our inward environmental landscape that affect our thoughts and actions. If outward and inward environments produce predictable responses, then we are not free to choose our responses here, either. How then is it possible to take any responsibility for our actions in response to these environmental pressures?
The key is in the phrase itself. Responsibility must be "taken" for our behaviours. It must be a conscious acknowledgement - it isn't a given. We can decide to take responsibility for our responses to the changes produced in us by our environment in the same way we take responsibility for a pet's behaviour when we decide to acquire one. Taking responsibility is a social agreement that produces a more stable society. The first time our dog bites someone as a fear response we may be surprised by it, but the dog's behaviour is still our responsibility, as is any damage done by the pet to others. This relatively arbitrary agreement to take responsibility in some areas produces trust in others.
Once we become aware that we have "bitten" (harmed) someone, we can apologize. We can say "I am sorry I bit you. I respond that way when I feel fear". The apology is retroactive as well as proactive - it acknowledges harm done in the past as well as providing a warning against future harms. This is an act of responsibility-taking.
Will you bite someone again when the same situation arises? The answer is; you don't know. The act of apologizing and taking responsibility for the previous bite becomes part of your memory of the situation. There was a motivation to bite, but now if you bite again, you know you've decided to take responsibility for the bite - and for the damage caused. This knowledge may change the decision to bite in the future if the motivation against biting is strong enough. Over time, the environmental changes you implement (the apology is now part of the equation) might change the behaviour. The wind of motivation to bite blows in one direction, pushing you along with it. The wind of consequence and apology blows in the opposite direction. If this wind is strong enough, the bite is prevented. Taking note of the changes and offering honest warnings about your potential behaviour in known situations is also a form of taking responsibility.
A) I bit someone B) I am biting someone C) I will bite someone in the future.
Above are 3 statements that are as accurate as possible. They too are a form of taking responsibility.
A) I bit someone B) I want to bite, but this time I didn't C) I may or may not bite in the future.
These three statements acknowledge a change in behaviour in the present and the possibility, but not the certainty, of change in the future.
If you bite but cannot or will not acknowledge the predictability of future bites, you are not taking responsibility. If you allow a biter who does not take responsibility near you, you may get bitten - and that is now your responsibility.
If you read and agree with the thesis of this article, then you can implement responsibility-taking as you see fit in your life. You can inform the people around you. This will change your social environment and introduce a new level of accountability for you, and for anyone else who makes these sorts of changes.
If you are in a relationship with someone whom you'd like to take more responsibility for their actions, they can read this article. From their response, you can determine how much responsibility they are likely to take. Once you know the level of personal responsibility they can accept, staying with them or leaving is a decision you can make that is informed by their response.
Staying with them or leaving is your responsibility. Staying with someone who has informed you that they will not take the level of responsibility you feel is necessary for a healthy relationship - either directly - "I'm not interested in taking responsibility" or indirectly - by not acknowledging the harm caused by their actions - isn't a good idea.
Take a moment to tune into how interested you are in showing this article to a partner, or potential partner. If you feel there is value in this approach, but it would be dismissed by your partner and therefore you hesitate to get them to read it, you may be in a relationship already with someone who's not able or willing to take the same level of responsibility for their actions as you'd like. Staying with them, or pursuing a relationship with them is now a decision on your part to accept a lack of responsibility in a partner, and therefore recriminations about their behaviour would be unwarranted and hypocritical. We, of course, have relationships with family or others that we cannot easily leave. Understanding the capacity for responsible action on their part may still benefit those relationships which cannot be left.
You can't actually get someone else to take responsibility - that isn't within the realm of responsibilities you could take. But by pointing the evolutionary power of iterative environmental pressures toward your own behaviour, your capacity to become more responsible in greater and greater areas of your life may increase.