Bethrothal is a marriage tradition that is almost exclusively practiced by the Hylian nobility, also known as the Honorable 24, that is used to ensure that their families continue, as well as to prevent their bloodlines from mixing with "undesirables". The practice involves families contracting their daughters to marry the sons of other family members at young ages for a dowry with the agreement that a marriage will take place the moment the girl is of age.
Bethrothal has been a known practice among the nobility for thousands of years, but it had recently become popular among the new nobility of the Kingdom of New Hyrule. Before the Calamity, betrothal was only practiced sparingly by less than 10% of the noble families. After the Calamity, however, well over 50% of the families engage in this custom. There are many reasons as to why, but the biggest seems to be that the nobility is so terrified of losing their place that they believe that this is the only way that they can control their bloodlines.
As control over the family affairs is generally passed onto the sons, noble daughters are essentially raised as bargaining chips to be exchanged with other families for clout. When a family believes that their daughter is old enough to understand the process, 10 years old at the minimum, they let the other families know that they have a girl who is available for marriage. At that point, a man from another family who is in the market for a wife will express his interest in the girl depending on a variety of factors. A non-exhaustive list of these factors can include beauty, health, the wealth and/or prestige of her family, acceptable mannerisms, and her ability to sell herself as an appropriate wife, and if the man is satisfied, a contract, known as a Betrothal Agreement, will be drawn between himself and the girl's father.
Components and tools
The Betrothal Agreement contract is a legal document that states that the daughter of Family X will marry a man of Family Y at a date that is set on or after the girl becomes the age of majority, which for Hylians is 17 years old. In exchange for the girl's hand, the family of the future groom offers to pay the girl's family a dowry, which can be anything from money to a shared ownership of a business to political favors. Once the contract is set (and perused by their counselors), it must be signed by a judge to make it binding. Once the judge agrees that nothing illegal is taking place and signs the document, the girl and the man are officially betrothed and legally bound to the conditions of the contract. It can only be dissolved if both families agree to do so.
On the business side of things, the tradition almost always involves the father of a girl making an agreement with a man interested in marrying his daughter, as well as the head of that man's household if that is not his position. It also involves the legal counsel of each family to ensure that nothing nefarious is sneaked into the contract, as well as the judge that must sign the contract to make it legally binding. On the other side, the daughter is groomed and coached by her mother and/or already-married sisters/other female family members on how best to be picked for marriage. The girl is extensively taught proper etiquette and self-grooming practices and is drilled heavily about her potential suitors so that she knows how best to please them. And most importantly of all, the girl is taught how to take care of her body so that she may successfully bear the children of her new husband.