Planning your nuptials necessitates a keen understanding of budgeting, particularly when it comes to selecting the symbol of your eternal love - your wedding bands. Navigating the labyrinth of design options, material choices, and pricing tiers can be a Herculean task. Utilizing principles from economics, mathematics, and statistics, this post aims to guide you on a step-by-step journey to budgeting for your perfect wedding bands.

The first step in this journey requires an understanding of the concept of opportunity cost, a cornerstone of economic theory. Opportunity cost refers to the potential benefits an individual, investor, or business misses out on when choosing one alternative over another. In the context of selecting your wedding bands, this implies the trade-off between the cost of the rings and other wedding expenses, or indeed, other life expenses. Your budget for wedding bands should thus be a balance between your personal preference and your resources, and the limitations they inherently impose.

The Pareto principle, or the 80/20 rule, which asserts that for many outcomes roughly 80% of consequences come from 20% of the causes, may also be a useful tool in your budgeting journey. In this case, 20% of your considerations (material, design, and price) could potentially influence 80% of your satisfaction with the final choice of wedding bands.

Subsequently, making a judicious choice of material for your wedding bands is pivotal. Traditionally, gold, silver, and platinum have been the choice of materials for wedding bands. However, contemporary couples often opt for alternative materials, such as titanium, tungsten, or even wood. Each of these materials has its own set of properties and price points, hence a comparative analysis is recommended. For instance, while gold rings offer a timeless appeal, titanium rings are more durable and scratch-resistant, and generally more cost-effective.

Next, consider the design of your wedding bands. The choices range from traditional plain bands to intricate designs studded with gemstones, engraved motifs, or unique finishes. From a game theory perspective, the design choice could be viewed as a coordination game, where the couple must coordinate their strategies (preferences) to arrive at a mutually beneficial outcome (the perfect wedding bands). The design of your rings should not only reflect your personal styles but also be a harmonious representation of your union.

The optimal budget for your wedding bands can be computed using decision theory principles. This theory utilizes mathematical models and statistical techniques to identify the values, uncertainties and other issues relevant in a given decision. In this scenario, your budget for the wedding bands would be the output of a decision-making process that takes into account your total wedding budget, the proportion of that you’re willing to allocate to the bands, and your preference ranking of the band material and design.

Where and when to purchase your wedding bands is also a strategic decision. The Law of One Price, an economic concept which posits that in an efficient market all identical goods must have only one price, may not hold in the case of wedding bands. The price of wedding bands can vary significantly based on the vendor and location. Thus, it's worth shopping around or even considering online vendors to ensure you're getting the best value.

Finally, keep in mind that while budgeting for your wedding bands is important, it is equally essential not to lose sight of what they symbolize. Economists often talk about intangible assets - non-physical assets that can't be seen, touched or physically measured, but are nonetheless valuable. The intrinsic value of your wedding bands - their representation of your love and commitment - far exceeds their monetary cost.

In conclusion, budgeting for your wedding bands is an exercise in strategic decision making, requiring careful consideration of economic principles, mathematical models, and statistical techniques. It’s a balancing act of personal preferences, financial resources, and market dynamics. But as with all things in life, remember to cherish the intangible over the tangible, for the value of love is beyond measure.