To repair damaged relationships with employees, these executives decided to say two of the toughest words for many bosses to utter: “I’m sorry.” Such mea culpas seem to be more common these days, partly because of the growing likelihood of a public uproar on social media when companies slip up.

Whatever the motivating factor, contrition is good for more than just the soul. Apologies can help restore a manager's credibility after a damaging error, and they also can inspire greater trust in management at a time when many workers are feeling disillusioned with employers. 

For example, about a third of UK employees characterise trust between them and senior management as weak, according to a study this year by the Chartered Institute of Personnel and Development, a human-resources organisation in London. Similarly, a global study by Forum Corp, a Boston-based consultancy, found that about one-third of workers trust business leaders less now than in the past. The managers in the survey were even more pessimistic: 43% said they believe employees trust bosses less now.

Honesty clearly is the cornerstone of trust, and that includes owning up to mistakes and apologising. Some respondents to the UK study said they would admire leaders if only they admitted their mistakes.

Beyond engendering trust, acknowledging an error and making amends can encourage greater openness throughout an organisation. “When leaders admit mistakes, its shows they’re human and vulnerable, and it makes it safe for others to talk about their mistakes, too,” said Dennis Reina, president of the Reina Trust Building Institute, a consulting firm based in Stowe, Vermont.

How common are apologies from bosses? It depends on whom you ask. Many employees believe managers don’t take responsibility for their screw-ups and don’t express regret. Only 19% of employees said their managers often or always apologise. But managers have quite different perceptions of their behaviour: 87% said they often or always say they’re sorry. But some managers said they don’t apologise because they don’t want to look weak or incompetent.

“When a leader makes a mistake like lying or taking credit for another employee’s idea and doesn’t apologise immediately, it begins to chip away at the trust the employee feels towards them,” said Andrew Graham, CEO of Forum. “This is true even if the employee observes this behaviour in his or her boss and isn’t the direct victim of the incident.”