All children want periods of undivided love and attention. No matter how much kids love their brothers and sisters, inevitably there will be periods of conflict and competition among siblings for parent's attention. Though such competition cannot be eliminated entirely, there are methods that parents can use to minimize or reduce sibling rivalry.
Distribute resources and restrictions equally
One method of reducing sibling conflict is for parents to take great care to spread their attention evenly across children such that no single child ends up with an "unfair" share. For practical and emotional reasons, this can be a difficult goal to accomplish. Each child has a unique needs and a unique personality. One child may have been born with an easier, less demanding temperament than another, or one child may have a medical issue that requires more care than other children. When these types of situations are the case, the less easy, more needy children naturally gain the lion's share of parents' attention. As well, parents are not perfect. Though they'd never admit it, they may in fact have favorite children. There is no exact way to spread parents' time and resources equally among all children in the family. However, parents should try their absolute best not to express blatant preferences, and to balance out built-in imbalances (such as might be caused by one child's medical issues) by providing extra attention for less needy children.
In a similar vein, parents should do what they can to not spend noticeably more time with a specific child, or provide them with substantially more resources or gifts compared with other children.
Any house rules and expectations that exist should be applied equally to all children, adjusting for children's different ages and competencies. It may be the case that Jane gets to stay outside later than Paul, but this can be justified if Jane is older and more mature than Paul. When Paul gets to be Jane's current age, he too can stay out later.
In addition, caregivers should be careful to not compare one child to another in a way that makes one appear "better" than another. For example, it is fine for Mom to say stuff like, "Jimmy, I'm so proud of your ability to hit a home run! I'm also proud of your sister Jill's ability to swim so fast!" It is not such a good idea for Mom to say "Jimmy! Why can't you be more like your sister and turn all your homework in on time?" Though it is likely not actually true that Jimmy's parents love his sister more than him, the latter statement sets Jimmy up to believe that his parents love is conditional on his performance. Upon hearing such a statement, he may easily and mistakenly conclude that he must measure up to his sister's level of academic performance before he can have his parent's approval and love. Though Jimmy's academics might (or might not) improve as a result of his developing a fear of his parents abandoning him, his mental health will likely suffer.